Users' Mathboxes Mathbox for Rodolfo Medina < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  an43OLD Unicode version

Theorem an43OLD 26713
Description: Rearrangement of 4 conjuncts. (Contributed by Rodolfo Medina, 24-Sep-2010.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
an43OLD  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  th ) )  <->  ( ( ph  /\  th )  /\  ( ps  /\  ch )
) )

Proof of Theorem an43OLD
StepHypRef Expression
1 ancom 437 . . 3  |-  ( ( ch  /\  th )  <->  ( th  /\  ch )
)
21anbi2i 675 . 2  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  th ) )  <->  ( ( ph  /\  ps )  /\  ( th  /\  ch )
) )
3 an4 797 . 2  |-  ( ( ( ph  /\  ps )  /\  ( th  /\  ch ) )  <->  ( ( ph  /\  th )  /\  ( ps  /\  ch )
) )
42, 3bitri 240 1  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  th ) )  <->  ( ( ph  /\  th )  /\  ( ps  /\  ch )
) )
Colors of variables: wff set class
Syntax hints:    <-> 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