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Theorem elim2if 23958
 Description: Elimination of two conditional operators contained in a wff . (Contributed by Thierry Arnoux, 25-Jan-2017.)
Hypotheses
Ref Expression
elim2if.1
elim2if.2
elim2if.3
Assertion
Ref Expression
elim2if

Proof of Theorem elim2if
StepHypRef Expression
1 exmid 405 . . 3
21biantrur 493 . 2
3 andir 839 . 2
4 iftrue 3705 . . . . 5
5 elim2if.1 . . . . 5
64, 5syl 16 . . . 4
76pm5.32i 619 . . 3
8 iffalse 3706 . . . . . . 7
98eqeq1d 2412 . . . . . 6
10 elim2if.2 . . . . . 6
119, 10syl6bir 221 . . . . 5
128eqeq1d 2412 . . . . . 6
13 elim2if.3 . . . . . 6
1412, 13syl6bir 221 . . . . 5
1511, 14elimifd 23957 . . . 4
1615pm5.32i 619 . . 3
177, 16orbi12i 508 . 2
182, 3, 173bitri 263 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:  elim2ifim  23959 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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