Theorem an13s 557

Description: Swap two conjuncts in antecedent. (Contributed by NM, 31-May-2006.)

Hypothesis

Ref	Expression
an12s.1	|- ( ( ph /\ ( ps /\ ch ) ) -> th )

Assertion

Ref	Expression
an13s	|- ( ( ch /\ ( ps /\ ph ) ) -> th )

Proof of Theorem an13s

Step	Hyp	Ref	Expression
1		an12s.1	. . . 4 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
2	1	exp32 363	. . 3 |- ( ph -> ( ps -> ( ch -> th ) ) )
3	2	com13 80	. 2 |- ( ch -> ( ps -> ( ph -> th ) ) )
4	3	imp32 255	1 |- ( ( ch /\ ( ps /\ ph ) ) -> th )

Syntax hints:   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem is referenced by: (None)