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Theorem iftruei 3475
Description: Inference associated with iftrue 3474. (Contributed by BJ, 7-Oct-2018.)
Hypothesis
Ref Expression
iftruei.1  |-  ph
Assertion
Ref Expression
iftruei  |-  if (
ph ,  A ,  B )  =  A

Proof of Theorem iftruei
StepHypRef Expression
1 iftruei.1 . 2  |-  ph
2 iftrue 3474 . 2  |-  ( ph  ->  if ( ph ,  A ,  B )  =  A )
31, 2ax-mp 5 1  |-  if (
ph ,  A ,  B )  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1331   ifcif 3469
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 2119
This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-if 3470
This theorem is referenced by:  ctmlemr  6986  xnegpnf  9604  xnegmnf  9605  xaddpnf1  9622  xaddpnf2  9623  xaddmnf1  9624  xaddmnf2  9625  pnfaddmnf  9626  mnfaddpnf  9627  iseqf1olemqk  10260  exp0  10290  sumsnf  11171  lcm0val  11735  ennnfonelemj0  11903  ennnfonelem0  11907  peano3nninf  13190
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