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Theorem iffalsei 4046
 Description: Inference associated with iffalse 4045. (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 4045 . 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 1475  ifcif 4036 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-if 4037 This theorem is referenced by:  sum0  14299  prod0  14512  prmo4  15673  prmo6  15675  itg0  23352  vieta1lem2  23870  vtxval0  25714  iedgval0  25715  ex-prmo  26708  dfrdg2  30945  dfrdg4  31228  fwddifnp1  31442  bj-pr21val  32194  bj-pr22val  32200  clsk1indlem4  37362  clsk1indlem1  37363  refsum2cnlem1  38219  iblempty  38857  fouriersw  39124
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