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Theorem iftruei 3480
 Description: Inference associated with iftrue 3479. (Contributed by BJ, 7-Oct-2018.)
Hypothesis
Ref Expression
iftruei.1 𝜑
Assertion
Ref Expression
iftruei if(𝜑, 𝐴, 𝐵) = 𝐴

Proof of Theorem iftruei
StepHypRef Expression
1 iftruei.1 . 2 𝜑
2 iftrue 3479 . 2 (𝜑 → if(𝜑, 𝐴, 𝐵) = 𝐴)
31, 2ax-mp 5 1 if(𝜑, 𝐴, 𝐵) = 𝐴
 Colors of variables: wff set class Syntax hints:   = wceq 1331  ifcif 3474 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in2 604  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-if 3475 This theorem is referenced by:  ctmlemr  6993  xnegpnf  9623  xnegmnf  9624  xaddpnf1  9641  xaddpnf2  9642  xaddmnf1  9643  xaddmnf2  9644  pnfaddmnf  9645  mnfaddpnf  9646  iseqf1olemqk  10279  exp0  10309  sumsnf  11190  lcm0val  11757  ennnfonelemj0  11925  ennnfonelem0  11929  peano3nninf  13308
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