Theorem an13s 778

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 588	. . 3 |- (ph -> (ps -> (ch -> th)))
3	2	com13 74	. 2 |- (ch -> (ps -> (ph -> th)))
4	3	imp32 422	1 |- ((ch /\ (ps /\ ph)) -> th)

Syntax hints:   -> wi 4   /\ wa 358

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 177  df-an 360

This theorem is referenced by: (None)