Theorem an31s 560

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

Hypothesis

Ref	Expression
an32s.1	|- ( ( ( ph /\ ps ) /\ ch ) -> th )

Assertion

Ref	Expression
an31s	|- ( ( ( ch /\ ps ) /\ ph ) -> th )

Proof of Theorem an31s

Step	Hyp	Ref	Expression
1		an32s.1	. . . 4 |- ( ( ( ph /\ ps ) /\ ch ) -> th )
2	1	exp31 362	. . 3 |- ( ph -> ( ps -> ( ch -> th ) ) )
3	2	com13 80	. 2 |- ( ch -> ( ps -> ( ph -> th ) ) )
4	3	imp31 254	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:  genpassl  7465  genpassu  7466