Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  impexp3acom3r Unicode version

Theorem impexp3acom3r 28277
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 28275 . 2  |-  ( (
ph  ->  ( ( ps 
/\  ch )  ->  th )
)  <->  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) ) )
2 com3rgbi 28276 . 2  |-  ( ( ps  ->  ( ch  ->  ( ph  ->  th )
) )  <->  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) ) )
31, 2bitr4i 243 1  |-  ( (
ph  ->  ( ( ps 
/\  ch )  ->  th )
)  <->  ( ps  ->  ( ch  ->  ( ph  ->  th ) ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ wa 358
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