Theorem 3com12d 32304

Description: Commutation in consequent. Swap 1st and 2nd. (Contributed by Jeff Hankins, 17-Nov-2009.)

Hypothesis

Ref	Expression
3com12d.1	|- ( ph -> ( ps /\ ch /\ th ) )

Assertion

Ref	Expression
3com12d	|- ( ph -> ( ch /\ ps /\ th ) )

Proof of Theorem 3com12d

Step	Hyp	Ref	Expression
1		3com12d.1	. 2 |- ( ph -> ( ps /\ ch /\ th ) )
2		id 22	. . 3 |- ( ( ch /\ ps /\ th ) -> ( ch /\ ps /\ th ) )
3	2	3com12 1269	. 2 |- ( ( ps /\ ch /\ th ) -> ( ch /\ ps /\ th ) )
4	1, 3	syl 17	1 |- ( ph -> ( ch /\ ps /\ th ) )

Syntax hints:   -> wi 4   /\ w3a 1037

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 197  df-an 386  df-3an 1039

This theorem is referenced by: (None)