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Theorem iffalsei 4535
Description: Inference associated with iffalse 4534. (Contributed by BJ, 7-Oct-2018.)
Hypothesis
Ref Expression
iffalsei.1 ¬ 𝜑
Assertion
Ref Expression
iffalsei if(𝜑, 𝐴, 𝐵) = 𝐵

Proof of Theorem iffalsei
StepHypRef Expression
1 iffalsei.1 . 2 ¬ 𝜑
2 iffalse 4534 . 2 𝜑 → if(𝜑, 𝐴, 𝐵) = 𝐵)
31, 2ax-mp 5 1 if(𝜑, 𝐴, 𝐵) = 𝐵
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3   = wceq 1540  ifcif 4525
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-if 4526
This theorem is referenced by:  ssttrcl  9755  ttrclselem2  9766  sum0  15757  prod0  15979  prmo4  17165  prmo6  17167  itg0  25815  vieta1lem2  26353  right1s  27934  vtxval0  29056  iedgval0  29057  ex-prmo  30478  dfrdg2  35796  dfrdg4  35952  fwddifnp1  36166  bj-pr21val  37014  bj-pr22val  37020  imsqrtvalex  43659  clsk1indlem4  44057  clsk1indlem1  44058  refsum2cnlem1  45042  limsup10ex  45788  iblempty  45980  fouriersw  46246
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