Metamath Proof Explorer

Theorem ancomstVD

Description: Closed form of ancoms . 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 |- ( ( ( ph /\ ps ) -> ch ) <-> ( ( ps /\ ph ) -> ch ) )
The proof of ancomst is derived automatically from it. (Contributed by Alan Sare, 25-Dec-2011) (Proof modification is discouraged.) (New usage is discouraged.)

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

Proof

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