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Theorem dfif2 3664
 Description: An alternate definition of the conditional operator df-if 3663 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 3663 . 2
2 df-or 359 . . . 4
3 orcom 376 . . . 4
4 iman 413 . . . . 5
54imbi1i 315 . . . 4
62, 3, 53bitr4i 268 . . 3
76abbii 2465 . 2
81, 7eqtri 2373 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wo 357   wa 358   wceq 1642   wcel 1710  cab 2339  cif 3662 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-if 3663 This theorem is referenced by:  iftrue  3668  nfifd  3685
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