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Theorem iffalsei 3451
Description: Inference associated with iffalse 3450. (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 3450 . 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 1314   ifcif 3442
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 587  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-11 1467  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-if 3443
This theorem is referenced by:  0tonninf  10152  sum0  11097  ennnfonelem1  11815
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