Theorem pm3.2an3 1083

Description: pm3.2 126 for a triple conjunction. (Contributed by Alan Sare, 24-Oct-2011.)

Assertion

Ref	Expression
pm3.2an3	|- ( ph -> ( ps -> ( ch -> ( ph /\ ps /\ ch ) ) ) )

Proof of Theorem pm3.2an3

Step	Hyp	Ref	Expression
1		pm3.2 126	. . 3 |- ( ( ph /\ ps ) -> ( ch -> ( ( ph /\ ps ) /\ ch ) ) )
2	1	ex 108	. 2 |- ( ph -> ( ps -> ( ch -> ( ( ph /\ ps ) /\ ch ) ) ) )
3		df-3an 887	. . 3 |- ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ps ) /\ ch ) )
4	3	bicomi 123	. 2 |- ( ( ( ph /\ ps ) /\ ch ) <-> ( ph /\ ps /\ ch ) )
5	2, 4	syl8ib 155	1 |- ( ph -> ( ps -> ( ch -> ( ph /\ ps /\ ch ) ) ) )

Syntax hints:   -> wi 4   /\ wa 97   /\ w3a 885

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110  df-3an 887

This theorem is referenced by:  3exp  1103