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Theorem dfif2 3943
Description: An alternate definition of the conditional operator df-if 3942 with one fewer connectives (but probably less intuitive to understand). (Contributed by NM, 30-Jan-2006.)
Assertion
Ref Expression
dfif2
Distinct variable groups:   ,   ,   ,

Proof of Theorem dfif2
StepHypRef Expression
1 df-if 3942 . 2
2 df-or 370 . . . 4
3 orcom 387 . . . 4
4 iman 424 . . . . 5
54imbi1i 325 . . . 4
62, 3, 53bitr4i 277 . . 3
76abbii 2591 . 2
81, 7eqtri 2486 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  \/wo 368  /\wa 369  =wceq 1395  e.wcel 1818  {cab 2442  ifcif 3941
This theorem is referenced by:  iftrue  3947  nfifd  3969
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-if 3942
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