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Theorem ibllem 22599
 Description: Conditioned equality theorem for the if statement. (Contributed by Mario Carneiro, 31-Jul-2014.)
Hypothesis
Ref Expression
ibllem.1
Assertion
Ref Expression
ibllem

Proof of Theorem ibllem
StepHypRef Expression
1 ibllem.1 . . . . 5
21breq2d 4438 . . . 4
32pm5.32da 645 . . 3
43ifbid 3937 . 2
51adantrr 721 . . 3
65ifeq1da 3945 . 2
74, 6eqtrd 2470 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 370   wceq 1437   wcel 1870  cif 3915   class class class wbr 4426  cc0 9538   cle 9675 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-rab 2791  df-v 3089  df-dif 3445  df-un 3447  df-in 3449  df-ss 3456  df-nul 3768  df-if 3916  df-sn 4003  df-pr 4005  df-op 4009  df-br 4427 This theorem is referenced by:  isibl  22600  isibl2  22601  iblitg  22603  iblcnlem1  22622  iblcnlem  22623  itgcnlem  22624  iblrelem  22625  itgrevallem1  22629  itgeqa  22648
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