Theorem pm3.2an3 1131

Description: pm3.2 434 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		pm3.2 434	. . 3 |- ((ph /\ ps) -> (ch -> ((ph /\ ps) /\ ch)))
2	1	ex 423	. 2 |- (ph -> (ps -> (ch -> ((ph /\ ps) /\ ch))))
3		df-3an 936	. . 3 |- ((ph /\ ps /\ ch) <-> ((ph /\ ps) /\ ch))
4	3	bicomi 193	. 2 |- (((ph /\ ps) /\ ch) <-> (ph /\ ps /\ ch))
5	2, 4	syl8ib 222	1 |- (ph -> (ps -> (ch -> (ph /\ ps /\ ch))))

Syntax hints:   -> wi 4   /\ wa 358   /\ w3a 934

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 177  df-an 360  df-3an 936

This theorem is referenced by:  3exp  1150