The Scriptures reveal that the believer's initial salvation includes both "righteousness" and "holiness":
"And that ye put on the new man, which after God is created in righteousness and true holiness" (Eph.4:24).
The Greek word translated righteousness can be defined as "the condition acceptable to God" (Thayer's Greek English Lexicon). The Greek word translated "justified" means "to declare, pronounce, one to be just, righteous, or such as he ought to be" (Thayer's Greek English Lexicon). So when the believer is "justified" he is declared to be in a condition acceptable to God.
Earlier it was shown that the believer is "justified by blood" (Ro.5:9). This means that the Lord God pronounces the believer to be in a condition acceptable to Him based on the blood of Christ. It was also shown that the symbolic meaning of the word "blood" is "death applied."
The believer is said to be "justified by blood" (Ro.5:9) and "justified by faith" (Ro.5:1). So when the believer applies the death of Christ to himself by faith the Lord God pronounces that he is in a condition acceptable to Him. The Lord Jesus died as the believer's substitute to bear the sentence of spiritual death on his behalf.
The root of the Greek word translated "holiness" at Ephesians 4:24 is hosios, and that word means "undefiled by sin" (Thayer's Greek English Lexicon). The believer is said to be sanctified by the blood of the covenant (Heb.10:29), and one of the meanings of the Greek word translated "sanctify" is "to purify" (Thayer's Greek English Lexicon).
Let us look at the "type" in regard to a believer's purification by the blood of the covenant.
"And he sent young men of the children of Israel, which offered burnt offerings, and sacrificed peace offerings of oxen unto the LORD...And Moses took the blood, and sprinkled it on the people, and said, Behold the blood of the covenant, which the LORD hath made with you concerning all these words" (Ex.19:5,8).
We can see from the following passages from the book of Hebrews that the blood of the covenant was in regard to a purification from defilement, the remission of sins:
"For when Moses had spoken every precept to all the people according to the law, he took the blood of calves and of goats, with water, and scarlet wool, and hyssop, and sprinkled both the book, and all the people, Saying, This is the blood of the covenant which God hath enjoined unto you...And almost all things are by the law purged with blood; and without shedding of blood is no remission. It was therefore necessary that the patterns of things in the heavens should be purified with these" (Heb.9:19-20,22-23).
Here we read that the things in regard to this "type" (pattern) were "purified" with the blood. Also,the Greek word translated "purged" in verse 22 means "to make clean" or "to pronounce clean in a levitical sense" (Thayer's Greek English Lexicon).
According the The New Scofield Study Bible the Greek word translated "remission" in verse 22 means "to send away":
"The Greek word here translated 'remission' (also in Acts 10:43; Heb.9:22), is elsewhere translated 'forgiveness.' It means, 'to send off' or 'away.' And this, throughout Scripture, is the one fundamental meaning of forgiveness--to separate the sin from the sinner" (The New Scofield Study Bible, note at Matthew 26:28).
So it was by the "blood," or when death was applied to these things that they were made "undefiled by sin." It was not until the blood of the covenant was sprinkled upon the people that the deaths of the sacrifices were applied to them. It was not until then that they were purified from their sins and therefore made a "holy" people.
This shows that their participation in the benefits of the death of the sacrifices (which were "types" of the Lord Jesus) depended upon the sprinkling of the blood of those sacrifices. This demonstrates that the death of the Lord Jesus on the Cross brings no santification to anyone until that death is applied by faith.
If the Lord Jesus died as a "substitute" for all men then all men would would receive the benefits of the death of the Lord Jesus in regard to the remission of sins. But from the words of the Lord Jesus here we can understand that His blood was shed for many and not for all:
"And he took the cup, and gave thanks, and gave it to them, saying, Drink ye all of it; For this is my blood of the new covenant, which is shed for (peri) many for the remission of sins" (Mt.26:27-28).
Here the Greek word translated "for" is peri and one of the meanings of that word is "for the benefit of or advantage of: Mt. xxvi. 28" (Thayer's Greek English Lexicon).
The blood of the Lord Jesus was shed "for the benefit" of many but not all. One of the benefits is the "remission of sins," and it is only those who "believe" that receive the remission of sins, as witnessed by the words of the Apostle Peter:
"And he commanded us to preach unto the people, and to testify that it is he which was ordained of God to be the Judge of quick and dead. To him give all the prophets witness, that through his name whosoever believeth in him shall receive remission of sins" (Acts 10:42-43).
It is not until the sinner believes the gospel that it can be said that his sins have been taken away and that the Lord Jesus bore his sins in His own body on the tree:
"Who His own self bare our sins in His own body on the tree, that we, being dead to sins, should live unto righteousness: by whose stripes ye were healed" (1 Peter 2:24).