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Theorem ifpbi1b 36117
 Description: When the first variable is irrelevant, it can be replaced. (Contributed by RP, 25-Apr-2020.)
Assertion
Ref Expression
ifpbi1b if- if-

Proof of Theorem ifpbi1b
StepHypRef Expression
1 id 22 . . . . 5
21olci 392 . . . 4
31olci 392 . . . 4
42, 3pm3.2i 456 . . 3
51olci 392 . . . 4
61olci 392 . . . 4
75, 6pm3.2i 456 . . 3
8 ifpim123g 36114 . . 3 if- if-
94, 7, 8mpbir2an 928 . 2 if- if-
101olci 392 . . . 4
1110, 5pm3.2i 456 . . 3
121olci 392 . . . 4
133, 12pm3.2i 456 . . 3
14 ifpim123g 36114 . . 3 if- if-
1511, 13, 14mpbir2an 928 . 2 if- if-
169, 15impbii 190 1 if- if-
 Colors of variables: wff setvar class Syntax hints:   wn 3   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: (None)
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