The main point is met completely by the expression in 1 Peter 1, " Sanctified unto... the sprinkling of the blood of Jesus Christ." We are born again to have a share in the value of Christ's blood and work. When the things are named together in scripture, sanctification is before justification. Ordinary language is very different. Righteousness is not so put, because it is the foundation of God's dealing in blessing with us, and bringing us, by that regeneration which sets us apart for Him, into the full acceptance of Christ. Grace reigns through righteousness. There is practical progress then in holiness.
The use of John 6 goes somewhat farther and differently into the matter. Chapter 5 had presented the Son of God as quickening whom He would. In the latter, it is sovereign life-giving; in the former, it is appropriation by faith, and this of the Son of man (that is, the Lord come in flesh). Hence He is the bread that cometh down from heaven. But it is not the Christ to the Jews, received as born on earth, but the Son of man (the Word made flesh) giving life to the world. He must be received in this character; and to receive Him in this character, in which alone is life, we cannot stop short of His death. We must eat His flesh and drink His blood. This is His death-the blood separate from the body. Incarnation is of no avail for life unless death comes in: otherwise there is no atonement, sin is not put away. " Except a corn of wheat fall into the ground and die, it abideth alone; but if it die, it bringeth forth much fruit." Eating the flesh comes first, because it is the first prominent point of incarnation-Christ come in flesh for man, for the world. Drinking the blood is added because this is available as a dead Christ-the blood out of the body. Hence the monstrous character of the refusal of the cup in Romanism, as well as the doctrine of concomitancy (that is, that the blood is in the bread or alleged body of Christ). The forbidding of blood in the Old Testament denoted that man in the flesh could not meddle with death. Life belongs to God. Our drinking Christ's blood shows that through His death we come in freed from flesh as dead; and that death thus is life and liberty to us, deliverance from the old man and its guilt too, to us who have received the quickening of John 5.