Users' Mathboxes Mathbox for Rodolfo Medina < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  an43 Structured version   Unicode version

Theorem an43 26695
Description: Rearrangement of 4 conjuncts. (Contributed by Rodolfo Medina, 24-Sep-2010.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)
Assertion
Ref Expression
an43  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  th ) )  <->  ( ( ph  /\  th )  /\  ( ps  /\  ch )
) )

Proof of Theorem an43
StepHypRef Expression
1 an42 799 . 2  |-  ( ( ( ph  /\  th )  /\  ( ps  /\  ch ) )  <->  ( ( ph  /\  ps )  /\  ( ch  /\  th )
) )
21bicomi 194 1  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  th ) )  <->  ( ( ph  /\  th )  /\  ( ps  /\  ch )
) )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    /\ wa 359
This theorem is referenced by:  an3  26697  prtlem15  26724
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