Redeemer of all mankind

The following is taken from "Theological Meditations" (see link on this page), a web site I have been following for several years. It gives my views on the extent of the atonement. I believe in special and definite atonement (also called "limited atonement") but this is not to say that I deny that there are universal aspects of the atonement (as I have before stated).

Tony Byrne, the site's administrator, gives this heading for the comments to follow - 

John Mayer’s (1583–1664) Explanation of the Redemption of All Mankind in the Catechism

Here are some things said by Mayer that I can endorse (highlighting mine):

"So according to Saint Augustine’s [Aug. de predest. Sanct. lib. 174.8] like exposition of another Scripture-phrase tending hereto: Christ may be called the Redeemer of all mankind: not because all are actually redeemed by him; but because no man is redeemed by any other but Christ only." (As cited here)

"When we say, he redeemed all Mankind, the meaning is, he is the only Redeemer of all men, who attain this great benefit of redemption and salvation, by no other, according to that memorable saying, There is none other name given under Heaven, whereby to be saved, but the name of Jesus [Acts 4:11]. Such as like better of the distinction (viz. He redeemed all men, that is, in regard of the sufficiency of that he did, and suffered; but not of the efficacy thereof) may follow it if they please: For the passion of Christ was suitable to his person, his person of infinite excellency could not be so abated, without infinite merit, accruing by such humiliation: his dying was more than equivalent to all the world’s perishing everlastingly in Hell. Whereupon in giving himself a ransom for sinful man, he is rightly said to have redeemed all mankind, for so much as he paid the full price of an universal redemption: And this is the same in sense with that saying of John, Behold the Lamb of God that takes away the sins of the world. John 1.29. Wicked men and unbelievers are not hereby secured; but more justly and deeply damned, as treading under foot the Son of God, and profaning his blood."

Again, I have affirmed for many years that the death and sacrifice of Christ was sufficient for the salvation of all men but efficient only for the elect.