Does 1 Timothy 4:10 Prove Universalism?

In 1 Timothy it is said: "For it is for this we labor and strive, because we have fixed our hope on the living God, who is the Savior of all men, especially of believers," (1 Timothy 4:10 NASB1995). Some universalists, i.e. people who believe all will be saved, have argued that this verse proves universalism for states that God saves all, especially believers. This would seem to indicate that even nonbelievers can be saved, but is this what the verse actually means?

Ellicott in his book Ellicott's Commentary for English Readers, notes: "These words, like the assertion of 1 Timothy 2:4, have been often pressed into the service of that school of kindly, but mistaken, interpreters, who ignore, or explain away, the plain doctrine of Holy Scripture which tells us there are those whose destruction from the presence of the Lord shall be everlasting, whose portion shall be the “second death” (2 Thessalonians 1:9; Revelation 21:8). These interpreters prefer to substitute in place of this terrible, but repeated declaration, their own perilous theories of universalism. Here the gracious words seem to affix a seal to the statement immediately preceding, which speaks of “the hope in the living God” as the source of all the labour and brave patience of the Lord’s true servants. The living God is also a loving God, the Saviour of all, if they would receive Him, and, undoubtedly, the Redeemer of those who accept His love and are faithful to His holy cause," (Ellicott).

Barnes also notes: "Who is the Saviour of all men - This must be understood as denoting that he is the Saviour of all people in some sense which differs from what is immediately affirmed - "especially of those that believe." There is something pertaining to "them" in regard to salvation which does not pertain to "all men." It cannot mean that he brings all people to heaven, "especially" those who believe - for this would be nonsense. And if he brings all people actually to heaven, how can it be "especially" true that he does this in regard to those who believe? Does it mean that he saves others "without" believing? But this would be contrary to the uniform doctrine of the Scriptures; see Mark 16:16. When, therefore, it is said that he "is the Saviour of 'all' people, 'especially' of those who believe," it must mean that there is a sense in which it is true that he may be called the Saviour of all people, while, at the same time, it is "actually" true that those only are saved who believe. This may be true in two respects:

(1) As he is the "Preserver" of people Job 7:20, for in this sense he may be said to "save" them from famine, and war, and peril - keeping them from day to day; compare Psalm 107:28;

(2) as he has "provided" salvation for all people. He is thus their Saviour - and may be called the common Saviour of all; that is, he has confined the offer of salvation to no one class of people; he has not limited the atonement to one division of the human race; and he actually saves all who are willing to be saved by him," (Barnes).

The Expositor's Greek Testament also notes: "... while God is potentially Saviour of all, He is actually Saviour of the πιστοί (i.e. believers)," (Harvard University).

Paul — the author of 1 Timothy — is in no way claiming all will be saved; rather, he notes that Jesus is the savior of all in that he died for all. Even so, merely because he died for all, this does not mean all will accept his sacrifice. If say a man was working at a pizzeria, and when someone ordered a pizza they threw it on the ground, this would not make the worker not a chef; rather, it would mean the work done was not received. Jesus makes pizzas for all of mankind; even so, not all may choose to eat his pizza. Jesus is still a cook or savior; even if they were rejected.

References:

Barnes' Notes on the New Testament. United Kingdom, Kregel Publications, 1962.

Ellicott's Bible Commentary, Volume 1. N.p., Delmarva Publications, Inc., 2015.

The Expositor's Greek Testament. United States, Dodd, Mead, 1900.