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Theorem bj-dfifc2 33120
 Description: This should be the alternate definition of "ifc" if "if-" enters the main part. (Contributed by BJ, 20-Sep-2019.)
Assertion
Ref Expression
bj-dfifc2
Distinct variable groups:   ,   ,   ,

Proof of Theorem bj-dfifc2
StepHypRef Expression
1 df-if 3933 . 2
2 ancom 450 . . . . 5
3 ancom 450 . . . . 5
42, 3orbi12i 521 . . . 4
54bicomi 202 . . 3
65abbii 2594 . 2
71, 6eqtri 2489 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wo 368   wa 369   wceq 1374   wcel 1762  cab 2445  cif 3932 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1961  ax-ext 2438 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-clab 2446  df-cleq 2452  df-clel 2455  df-if 3933 This theorem is referenced by:  bj-df-ifc  33121
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