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Theorem dfif6 3887
 Description: An alternate definition of the conditional operator df-if 3885 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 3716 . 2
2 df-rab 2762 . . 3
3 df-rab 2762 . . 3
42, 3uneq12i 3594 . 2
5 df-if 3885 . 2
61, 4, 53eqtr4ri 2442 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wo 366   wa 367   wceq 1405   wcel 1842  cab 2387  crab 2757   cun 3411  cif 3884 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380 This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-rab 2762  df-v 3060  df-un 3418  df-if 3885 This theorem is referenced by:  ifeq1  3888  ifeq2  3889  dfif3  3898
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