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Theorem dfif6 3944
Description: An alternate definition of the conditional operator df-if 3942 as a simple class abstraction. (Contributed by Mario Carneiro, 8-Sep-2013.)
Assertion
Ref Expression
dfif6
Distinct variable groups:   ,   ,   ,

Proof of Theorem dfif6
StepHypRef Expression
1 unab 3764 . 2
2 df-rab 2816 . . 3
3 df-rab 2816 . . 3
42, 3uneq12i 3655 . 2
5 df-if 3942 . 2
61, 4, 53eqtr4ri 2497 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  \/wo 368  /\wa 369  =wceq 1395  e.wcel 1818  {cab 2442  {crab 2811  u.cun 3473  ifcif 3941
This theorem is referenced by:  ifeq1  3945  ifeq2  3946  dfif3  3955
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rab 2816  df-v 3111  df-un 3480  df-if 3942
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