Theorem an31s 848

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 630	. . 3 |- ( ph -> ( ps -> ( ch -> th ) ) )
3	2	com13 88	. 2 |- ( ch -> ( ps -> ( ph -> th ) ) )
4	3	imp31 448	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:  icoopnst  22738  grpoidinvlem3  27360  kbop  28812  frmin  31739  bddiblnc  33480