Theorem ancom1s 569

Description: Inference commuting a nested conjunction in antecedent. (Contributed by NM, 24-May-2006.) (Proof shortened by Wolf Lammen, 24-Nov-2012.)

Hypothesis

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

Assertion

Ref	Expression
ancom1s	|- ( ( ( ps /\ ph ) /\ ch ) -> th )

Proof of Theorem ancom1s

Step	Hyp	Ref	Expression
1		pm3.22 265	. 2 |- ( ( ps /\ ph ) -> ( ph /\ ps ) )
2		an32s.1	. 2 |- ( ( ( ph /\ ps ) /\ ch ) -> th )
3	1, 2	sylan 283	1 |- ( ( ( ps /\ ph ) /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem is referenced by:  bilukdc  1396  prarloc  7504  leltadd  8406  divmul13ap  8674  modqmulmodr  10392  fzomaxdif  11124  lgsdir2  14519