Theorem ancomsimp 1369

Description: Closed form of ancoms 264. (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 262	. 2 |- ( ( ph /\ ps ) <-> ( ps /\ ph ) )
2	1	imbi1i 236	1 |- ( ( ( ph /\ ps ) -> ch ) <-> ( ( ps /\ ph ) -> ch ) )

Syntax hints:   -> wi 4   /\ wa 102   <-> wb 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  ralcomf  2515