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Theorem iftrue 3336
 Description: Value of the conditional operator when its first argument is true. (Contributed by NM, 15-May-1999.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
iftrue

Proof of Theorem iftrue
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dedlema 876 . . 3
21abbi2dv 2156 . 2
3 df-if 3332 . 2
42, 3syl6reqr 2091 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 97   wo 629   wceq 1243   wcel 1393  cab 2026  cif 3331 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in2 545  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-if 3332 This theorem is referenced by:  iftruei  3337  iftrued  3338  ifbothdc  3357  ifcldcd  3358  fidifsnen  6331  uzin  8505  fzprval  8944  fztpval  8945  expival  9257
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