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Theorem elimifd 23957
 Description: Elimination of a conditional operator contained in a wff . (Contributed by Thierry Arnoux, 25-Jan-2017.)
Hypotheses
Ref Expression
elimifd.1
elimifd.2
Assertion
Ref Expression
elimifd

Proof of Theorem elimifd
StepHypRef Expression
1 exmid 405 . . . 4
21biantrur 493 . . 3
32a1i 11 . 2
4 andir 839 . . 3
54a1i 11 . 2
6 iftrue 3705 . . . . 5
7 elimifd.1 . . . . 5
86, 7syl5 30 . . . 4
98pm5.32d 621 . . 3
10 iffalse 3706 . . . . 5
11 elimifd.2 . . . . 5
1210, 11syl5 30 . . . 4
1312pm5.32d 621 . . 3
149, 13orbi12d 691 . 2
153, 5, 143bitrd 271 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wo 358   wa 359   wceq 1649  cif 3699 This theorem is referenced by:  elim2if  23958 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-if 3700
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