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Theorem iffalsei 3558
Description: Inference associated with iffalse 3557. (Contributed by BJ, 7-Oct-2018.)
Hypothesis
Ref Expression
iffalsei.1  |-  -.  ph
Assertion
Ref Expression
iffalsei  |-  if (
ph ,  A ,  B )  =  B

Proof of Theorem iffalsei
StepHypRef Expression
1 iffalsei.1 . 2  |-  -.  ph
2 iffalse 3557 . 2  |-  ( -. 
ph  ->  if ( ph ,  A ,  B )  =  B )
31, 2ax-mp 5 1  |-  if (
ph ,  A ,  B )  =  B
Colors of variables: wff set class
Syntax hints:   -. wn 3    = wceq 1364   ifcif 3549
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in2 616  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-11 1517  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-if 3550
This theorem is referenced by:  0tonninf  10469  sum0  11427  prod0  11624  ennnfonelem1  12457  dcapnconst  15263
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