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Theorem impexp3acom3r 28598
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. The completed Virtual Deduction Proof (not shown) was minimized. The minimized proof is shown. (Contributed by Alan Sare, 18-Mar-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
1::  |-  ( ( ph  ->  ( ( ps  /\  ch )  ->  th ) )  <->  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) ) )
2::  |-  ( ( ps  ->  ( ch  ->  ( ph  ->  th ) ) )  <->  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) ) )
qed:1,2:  |-  ( ( ph  ->  ( ( ps  /\  ch )  ->  th ) )  <->  ( ps  ->  ( ch  ->  ( ph  ->  th ) ) ) )
Assertion
Ref Expression
impexp3acom3r  |-  ( (
ph  ->  ( ( ps 
/\  ch )  ->  th )
)  <->  ( ps  ->  ( ch  ->  ( ph  ->  th ) ) ) )

Proof of Theorem impexp3acom3r
StepHypRef Expression
1 impexp3a 28596 . 2  |-  ( (
ph  ->  ( ( ps 
/\  ch )  ->  th )
)  <->  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) ) )
2 com3rgbi 28597 . 2  |-  ( ( ps  ->  ( ch  ->  ( ph  ->  th )
) )  <->  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) ) )
31, 2bitr4i 244 1  |-  ( (
ph  ->  ( ( ps 
/\  ch )  ->  th )
)  <->  ( ps  ->  ( ch  ->  ( ph  ->  th ) ) ) )
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