Theorem ancomsimp 1369

Description: Closed form of ancoms 439. Derived automatically from ancomsimpVD in set.mm. (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 437	. 2 |- ((ph /\ ps) <-> (ps /\ ph))
2	1	imbi1i 315	1 |- (((ph /\ ps) -> ch) <-> ((ps /\ ph) -> ch))

Syntax hints:   -> wi 4   <-> wb 176   /\ wa 358

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 177  df-an 360

This theorem is referenced by:  exp3acom23g  1371  ralcomf  2770