Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj432 Structured version   Unicode version

Theorem bnj432 29080
Description:  /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj432  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ( ch  /\  th )  /\  ( ph  /\  ps )
) )

Proof of Theorem bnj432
StepHypRef Expression
1 bnj422 29079 . 2  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ch  /\ 
th  /\  ph  /\  ps ) )
2 bnj256 29070 . 2  |-  ( ( ch  /\  th  /\  ph 
/\  ps )  <->  ( ( ch  /\  th )  /\  ( ph  /\  ps )
) )
31, 2bitri 241 1  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ( ch  /\  th )  /\  ( ph  /\  ps )
) )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    /\ wa 359    /\ w-bnj17 29050
This theorem is referenced by:  bnj605  29278  bnj600  29290
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  df-3an 938  df-bnj17 29051
  Copyright terms: Public domain W3C validator