Romans 14:7-8: "7 For none of us lives to himself, and none of us dies to himself. 8 For if we live, we live to the Lord, and if we die, we die to the Lord. So then, whether we live or whether we die, we are the Lord's."
2 Corinthians 1:9-10: "9 Indeed, we felt that we had received the sentence of death. But that was to make us rely not on ourselves but on God who raises the dead. 10 He delivered us from such a deadly peril, and he will deliver us. On him we have set our hope that he will deliver us again."
1 Corinthians 15:53-54: "53 For this perishable body must put on the imperishable, and this mortal body must put on immortality. 54 When the perishable puts on the imperishable, and the mortal puts on immortality, then shall come to pass the saying that is written: 'Death is swallowed up in victory.'"
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The passage from 2 Corinthians 1, specifically the reliance on God and His deliverance, appears in every verse: "Who shall help us in the strife / Lest the foe confound us? / Thou only, Lord, Thou only!" in the first, "Who will help when they assail, / Who secure will make us? / Thou only, Lord, Thou only!" in the second, and "Where shall we for refuge go, / Where for grace to bless us? / To Thee, Lord Jesus, only!" in the third.
It's unclear where exactly the other two passages show up. My best guess is that both are behind the lines "Lord, preserve and keep us / In the peace that faith can give" near the end of the third verse.
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The line "Snares of death surround us" near the beginning of the first verse is drawn from Psalm 18:4-5: "4 The cords of death encompassed me; the torrents of destruction assailed me; 5 the cords of Sheol entangled me; the snares of death confronted me."
The line "In the midst of death's dark vale" at the beginning of the second verse alludes to Psalm 23:4: "Even though I walk through the valley of the shadow of death, I will fear no evil, for you are with me; your rod and your staff, they comfort me."