Theorem impbidd 16227

Description: Lemma for prter3 16286.

Hypotheses

Ref	Expression
impbidd.1	|- (ph -> (ps -> (ch -> th)))
impbidd.2	|- (ph -> (ps -> (th -> ch)))

Assertion

Ref	Expression
impbidd	|- (ph -> (ps -> (ch <-> th)))

Proof of Theorem impbidd

Step	Hyp	Ref	Expression
1		impbidd.1	. . . 4 |- (ph -> (ps -> (ch -> th)))
2	1	imp 377	. . 3 |- ((ph /\ ps) -> (ch -> th))
3		impbidd.2	. . . 4 |- (ph -> (ps -> (th -> ch)))
4	3	imp 377	. . 3 |- ((ph /\ ps) -> (th -> ch))
5	2, 4	impbid 574	. 2 |- ((ph /\ ps) -> (ch <-> th))
6	5	ex 402	1 |- (ph -> (ps -> (ch <-> th)))

Syntax hints:   -> wi 3   <-> wb 163   /\ wa 240

This theorem is referenced by:  prtlem10 16265

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 164  df-an 242

Copyright terms: Public domain