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Theorem ifptru 1431
 Description: Value of the conditional operator for propositions when its first argument is true. Analogue for propositions of iftrue 3921. This is essentially dedlema 962. (Contributed by BJ, 20-Sep-2019.) (Proof shortened by Wolf Lammen, 10-Jul-2020.)
Assertion
Ref Expression
ifptru if-

Proof of Theorem ifptru
StepHypRef Expression
1 biimt 336 . 2
2 orc 386 . . . 4
32biantrud 509 . . 3
4 dfifp3 1423 . . 3 if-
53, 4syl6bbr 266 . 2 if-
61, 5bitr2d 257 1 if-
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wo 369   wa 370  if-wif 1420 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-ifp 1421 This theorem is referenced by:  ifpfal  1432  ifpid  1433  bj-elimhyp  30938  bj-dedthm  30939
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