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Theorem dfif6 3473
 Description: An alternate definition of the conditional operator df-if 3471 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 3342 . 2
2 df-rab 2516 . . 3
3 df-rab 2516 . . 3
42, 3uneq12i 3237 . 2
5 df-if 3471 . 2
61, 4, 53eqtr4ri 2284 1
 Colors of variables: wff set class Syntax hints:   wn 5   wo 359   wa 360   wceq 1619   wcel 1621  cab 2239  crab 2512   cun 3076  cif 3470 This theorem is referenced by:  ifeq1  3474  ifeq2  3475  dfif3  3480 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-rab 2516  df-v 2729  df-un 3083  df-if 3471
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