Theorem an31s 781

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 587	. . 3 |- (ph -> (ps -> (ch -> th)))
3	2	com13 74	. 2 |- (ch -> (ps -> (ph -> th)))
4	3	imp31 421	1 |- (((ch /\ ps) /\ ph) -> th)

This proof depends on syntax axioms:   -> wi 4   /\ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360

This theorem is used by: (None)