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Theorem elimif 3973
 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 3945 . . 3
2 elimif.1 . . 3
31, 2syl 16 . 2
4 iffalse 3948 . . 3
5 elimif.2 . . 3
64, 5syl 16 . 2
73, 6cases 969 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 184   wo 368   wa 369   wceq 1379  cif 3939 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-if 3940 This theorem is referenced by:  eqif  3977  elif  3979  ifel  3980  ftc1anclem5  29671
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