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Theorem elimif 3975
 Description: Elimination of a conditional operator contained in a wff . (Contributed by NM, 15-Feb-2005.) (Proof shortened by NM, 25-Apr-2019.)
Hypotheses
Ref Expression
elimif.1
elimif.2
Assertion
Ref Expression
elimif

Proof of Theorem elimif
StepHypRef Expression
1 iftrue 3947 . . 3
2 elimif.1 . . 3
31, 2syl 16 . 2
4 iffalse 3950 . . 3
5 elimif.2 . . 3
64, 5syl 16 . 2
73, 6cases 970 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  <->wb 184  \/wo 368  /\wa 369  =wceq 1395  ifcif 3941 This theorem is referenced by:  eqif  3979  elif  3981  ifel  3982  ftc1anclem5  30094 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-if 3942
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