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Theorem dfif2 3743
 Description: An alternate definition of the conditional operator df-if 3742 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 3742 . 2
2 df-or 361 . . . 4
3 orcom 378 . . . 4
4 iman 415 . . . . 5
54imbi1i 317 . . . 4
62, 3, 53bitr4i 270 . . 3
76abbii 2550 . 2
81, 7eqtri 2458 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wo 359   wa 360   wceq 1653   wcel 1726  cab 2424  cif 3741 This theorem is referenced by:  iftrue  3747  nfifd  3764 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 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 2425  df-cleq 2431  df-if 3742
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