Yes, it is. That means that a Christian once save cannot lose their salvation. And yes that is direct from the pages of the Bible. Here is some scripture that buttresses the position of “once saved”:
Hebrews 13: 5 (NASB)
5 Make sure that your character is free from the love of money, being content with what you have; for He Himself has said, “I will never desert you, nor will I ever forsake you,”
No one will take us out of God’s hand.
1 John 2: 19 (NASB)
They went out from us, but they were not really of us; for if they had been of us, they would have remained with us; but they went out, so that it would be shown that they all are not of us.
Those who are with Him will not be discarded.
If people choose to leave God’s salvation, they “chose” to leave. So if they were in fact regenerated Christians they would not have decided to leave, nor could they leave, thus losing their salvation! There Salvation is the crux of the matter! A regenerate Christian cannot lose their salvation, just put.
Beware this is not permission for the regenerate Christian to sin. Read Romans 6: 1-2 (NASB)
What shall we say then? Are we to continue in sin so that grace may increase? 2 May it never be! How shall we who died to sin still live in it?
The regenerate Christian is a changed person aka “born again”. Read 2 Corinthians 5: 16-17 (NASB)
16 Therefore from now on we recognize no one according to the flesh; even though we have known Christ according to the flesh, yet now we know Him in this way no longer. 17 Therefore if anyone is in Christ, he is a new creature; the old things passed away; behold, new things have come.
We cannot call Paul a liar, we do if we say that you can lose your salvation.
1 John 2: 3-4 (NASB)
3 By this we know that we have come to know Him, if we keep His commandments. 4 The one who says, “I have come to know Him,” and does not keep His commandments, is a liar, and the truth is not in him;
As a believer in election/predestination (written about in great detail in the biblical pages) I pray that the Holy Spirit saves those who are not the elect (as we do not ultimately know).