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Theorem iffalsei 4438
Description: Inference associated with iffalse 4437. (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 4437 . 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 1538  ifcif 4428
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2114  ax-9 2122  ax-ext 2773
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-sb 2070  df-clab 2780  df-cleq 2794  df-clel 2873  df-if 4429
This theorem is referenced by:  sum0  15074  prod0  15293  prmo4  16457  prmo6  16459  itg0  24387  vieta1lem2  24911  vtxval0  26836  iedgval0  26837  ex-prmo  28248  dfrdg2  33154  dfrdg4  33526  fwddifnp1  33740  bj-pr21val  34450  bj-pr22val  34456  imsqrtvalex  40343  clsk1indlem4  40744  clsk1indlem1  40745  refsum2cnlem1  41663  limsup10ex  42412  iblempty  42604  fouriersw  42870
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