Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj446 Structured version   Unicode version

Theorem bnj446 29474
Description:  /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj446  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ( ps  /\  ch  /\  th )  /\  ph ) )

Proof of Theorem bnj446
StepHypRef Expression
1 bnj345 29471 . 2  |-  ( ( ps  /\  ch  /\  th 
/\  ph )  <->  ( ph  /\ 
ps  /\  ch  /\  th ) )
2 df-bnj17 29444 . 2  |-  ( ( ps  /\  ch  /\  th 
/\  ph )  <->  ( ( ps  /\  ch  /\  th )  /\  ph ) )
31, 2bitr3i 254 1  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ( ps  /\  ch  /\  th )  /\  ph ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 187    /\ wa 370    /\ w3a 982    /\ w-bnj17 29443
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 188  df-an 372  df-3an 984  df-bnj17 29444
This theorem is referenced by:  bnj642  29510  bnj667  29514  bnj594  29675
  Copyright terms: Public domain W3C validator