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Theorem elimif 3760
 Description: Elimination of a conditional operator contained in a wff . (Contributed by NM, 15-Feb-2005.)
Hypotheses
Ref Expression
elimif.1
elimif.2
Assertion
Ref Expression
elimif

Proof of Theorem elimif
StepHypRef Expression
1 exmid 405 . . 3
21biantrur 493 . 2
3 andir 839 . 2
4 iftrue 3737 . . . . 5
5 elimif.1 . . . . 5
64, 5syl 16 . . . 4
76pm5.32i 619 . . 3
8 iffalse 3738 . . . . 5
9 elimif.2 . . . . 5
108, 9syl 16 . . . 4
1110pm5.32i 619 . . 3
127, 11orbi12i 508 . 2
132, 3, 123bitri 263 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wo 358   wa 359   wceq 1652  cif 3731 This theorem is referenced by:  eqif  3764  elif  3765  ifel  3766  ftc1anclem5  26274 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-if 3732
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