Theorem syl6com 35

Description: Syllogism inference with commuted antecedents. (Contributed by NM, 25-May-2005.)

Hypotheses

Ref	Expression
syl6com.1	|- ( ph -> ( ps -> ch ) )
syl6com.2	|- ( ch -> th )

Assertion

Ref	Expression
syl6com	|- ( ps -> ( ph -> th ) )

Proof of Theorem syl6com

Step	Hyp	Ref	Expression
1		syl6com.1	. . 3 |- ( ph -> ( ps -> ch ) )
2		syl6com.2	. . 3 |- ( ch -> th )
3	1, 2	syl6 33	. 2 |- ( ph -> ( ps -> th ) )
4	3	com12 30	1 |- ( ps -> ( ph -> th ) )

Syntax hints:   -> wi 4

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

This theorem is referenced by:  pclem6  1393  spimh  1759  ax16  1835  ax16i  1880  elres  4992  funcnvuni  5337  funrnex  6189  negf1o  8436  lidrididd  13132  dfgrp2  13277  rngdi  13620  rngdir  13621  basis2  14438  bj-inf2vnlem2  15771