Loraine Boettner, the Reformed theologian, made an important point when he said, "This doctrine does not stand alone but is a necessary part of the Calvinistic system of theology. The doctrines of Election and Efficacious Grace logically imply the certain salvation of those who receive these blessings. If God has chosen men absolutely and unconditionally to eternal life, and if His Spirit effectively applies to them the benefits of redemption, the inescapable conclusion is that these persons shall be saved."
The Westminster Confession of Faith adds this: "They, whom God has accepted in His Beloved, effectively called, and sanctified by His Spirit, can neither totally nor finally fall away from the state of grace, but shall certainly persevere therein to the end, and be eternally saved." Chapter 17, Paragraph 1
There is a plethora of Scripture that teach this doctrine. Consider these few verses:
For the mountains may be removed and the hills may shake, but My lovingkindness will not be removed from you, and My covenant of peace will not be shaken, says the Lord who has compassion on you. Isaiah 54:10
For I am confident of this very thing, that He who began a good work in you will perfect it until the day of Christ Jesus. Philippians 1:6
Now to Him who is able to keep you from stumbling, and to make you stand in the presence of His glory blameless with great joy, to the only God our Savior, through Jesus Christ our Lord, be glory, majesty, dominion and authority, before all time and now and forever. Amen. Jude 24, 25