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Theorem iffalsei 4094
 Description: Inference associated with iffalse 4093. (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 4093 . 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 1482  ifcif 4084 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1721  ax-4 1736  ax-5 1838  ax-6 1887  ax-7 1934  ax-9 1998  ax-10 2018  ax-11 2033  ax-12 2046  ax-13 2245  ax-ext 2601 This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1485  df-ex 1704  df-nf 1709  df-sb 1880  df-clab 2608  df-cleq 2614  df-clel 2617  df-if 4085 This theorem is referenced by:  sum0  14446  prod0  14667  prmo4  15829  prmo6  15831  itg0  23540  vieta1lem2  24060  vtxval0  25925  iedgval0  25926  ex-prmo  27300  dfrdg2  31685  dfrdg4  32042  fwddifnp1  32256  bj-pr21val  32985  bj-pr22val  32991  clsk1indlem4  38168  clsk1indlem1  38169  refsum2cnlem1  39022  limsup10ex  39805  iblempty  39950  fouriersw  40217
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