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Theorem ancomsimpVD 28914
Description: Closed form of ancoms 440. 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,?: e0_ 28821  |-  ( ( ( ph  /\  ps )  ->  ch )  <->  ( ( ps  /\  ph )  ->  ch ) )
(Contributed by Alan Sare, 25-Dec-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ancomsimpVD  |-  ( ( ( ph  /\  ps )  ->  ch )  <->  ( ( ps  /\  ph )  ->  ch ) )

Proof of Theorem ancomsimpVD
StepHypRef Expression
1 ancom 438 . 2  |-  ( (
ph  /\  ps )  <->  ( ps  /\  ph )
)
2 imbi1 314 . 2  |-  ( ( ( ph  /\  ps ) 
<->  ( ps  /\  ph ) )  ->  (
( ( ph  /\  ps )  ->  ch )  <->  ( ( ps  /\  ph )  ->  ch ) ) )
31, 2e0_ 28821 1  |-  ( ( ( ph  /\  ps )  ->  ch )  <->  ( ( ps  /\  ph )  ->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177    /\ wa 359
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 178  df-an 361
  Copyright terms: Public domain W3C validator