Theorem an13s 845

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 631	. . 3 |- ( ph -> ( ps -> ( ch -> th ) ) )
3	2	com13 88	. 2 |- ( ch -> ( ps -> ( ph -> th ) ) )
4	3	imp32 449	1 |- ( ( ch /\ ( ps /\ ph ) ) -> th )

Syntax hints:   -> wi 4   /\ wa 384

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

This theorem is referenced by:  cusgrfilem1  26351  abfmpeld  29454