Theorem ancomsimp 1428

Description: Closed form of ancoms 266. (Contributed by Alan Sare, 31-Dec-2011.)

Assertion

Ref	Expression
ancomsimp	|- ( ( ( ph /\ ps ) -> ch ) <-> ( ( ps /\ ph ) -> ch ) )

Proof of Theorem ancomsimp

Step	Hyp	Ref	Expression
1		ancom 264	. 2 |- ( ( ph /\ ps ) <-> ( ps /\ ph ) )
2	1	imbi1i 237	1 |- ( ( ( ph /\ ps ) -> ch ) <-> ( ( ps /\ ph ) -> ch ) )

Syntax hints:   -> wi 4   /\ wa 103   <-> wb 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  ralcomf  2627