Theorem ancomstVD 39101

Description: Closed form of ancoms 469. The following user's proof is completed by invoking mmj2's unify command and using mmj2's StepSelector to pick all remaining steps of the Metamath proof.

1::	|- ( ( ph /\ ps ) <-> ( ps /\ ph ) )
qed:1,?: e0a 38999	|- ( ( ( ph /\ ps ) -> ch ) <-> ( ( ps /\ ph ) -> ch ) )

The proof of ancomst 468 is derived automatically from it. (Contributed by Alan Sare, 25-Dec-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

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

Proof of Theorem ancomstVD

Step	Hyp	Ref	Expression
1		ancom 466	. 2 |- ( ( ph /\ ps ) <-> ( ps /\ ph ) )
2		imbi1 337	. 2 |- ( ( ( ph /\ ps ) <-> ( ps /\ ph ) ) -> ( ( ( ph /\ ps ) -> ch ) <-> ( ( ps /\ ph ) -> ch ) ) )
3	1, 2	e0a 38999	1 |- ( ( ( ph /\ ps ) -> ch ) <-> ( ( ps /\ ph ) -> ch ) )

Syntax hints:   -> wi 4   <-> wb 196   /\ 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: (None)