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Theorem dfif6 3766
 Description: An alternate definition of the conditional operator df-if 3764 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 3593 . 2
2 df-rab 2720 . . 3
3 df-rab 2720 . . 3
42, 3uneq12i 3485 . 2
5 df-if 3764 . 2
61, 4, 53eqtr4ri 2473 1
 Colors of variables: wff set class Syntax hints:   wn 3   wo 359   wa 360   wceq 1653   wcel 1727  cab 2428  crab 2715   cun 3304  cif 3763 This theorem is referenced by:  ifeq1  3767  ifeq2  3768  dfif3  3773 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-rab 2720  df-v 2964  df-un 3311  df-if 3764
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