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Theorem iftruei 3450
Description: Inference associated with iftrue 3449. (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 3449 . 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 1316   ifcif 3444
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 589  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-11 1469  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-if 3445
This theorem is referenced by:  ctmlemr  6961  xnegpnf  9579  xnegmnf  9580  xaddpnf1  9597  xaddpnf2  9598  xaddmnf1  9599  xaddmnf2  9600  pnfaddmnf  9601  mnfaddpnf  9602  iseqf1olemqk  10235  exp0  10265  sumsnf  11146  lcm0val  11673  ennnfonelemj0  11841  ennnfonelem0  11845  peano3nninf  13128
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