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Theorem dfif6 3568
 Description: An alternate definition of the conditional operator df-if 3566 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 3435 . 2
2 df-rab 2552 . . 3
3 df-rab 2552 . . 3
42, 3uneq12i 3327 . 2
5 df-if 3566 . 2
61, 4, 53eqtr4ri 2314 1
 Colors of variables: wff set class Syntax hints:   wn 3   wo 357   wa 358   wceq 1623   wcel 1684  cab 2269  crab 2547   cun 3150  cif 3565 This theorem is referenced by:  ifeq1  3569  ifeq2  3570  dfif3  3575 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-rab 2552  df-v 2790  df-un 3157  df-if 3566
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