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Theorem impexp3a 27648
Description: The following User's Proof is a Virtual Deduction proof completed automatically by the tools program completeusersproof.cmd, which invokes Mel O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. After the User's Proof was completed it was minimized. The completed User's Proof before minimization is not shown. (Contributed by Alan Sare, 18-Mar-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
1::  |-  ( ( ( ps  /\  ch )  ->  th )  <->  ( ps  ->  ( ch  ->  th ) ) )
qed:1:  |-  ( ( ph  ->  ( ( ps  /\  ch )  ->  th ) )  <->  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) ) )
Assertion
Ref Expression
impexp3a  |-  ( (
ph  ->  ( ( ps 
/\  ch )  ->  th )
)  <->  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) ) )

Proof of Theorem impexp3a
StepHypRef Expression
1 impexp 433 . 2  |-  ( ( ( ps  /\  ch )  ->  th )  <->  ( ps  ->  ( ch  ->  th )
) )
21imbi2i 303 1  |-  ( (
ph  ->  ( ( ps 
/\  ch )  ->  th )
)  <->  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ wa 358
This theorem is referenced by:  impexp3acom3r  27650
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 177  df-an 360
  Copyright terms: Public domain W3C validator