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Theorem 3anan12 947
Description: Convert triple conjunction to conjunction, then commute. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Andrew Salmon, 14-Jun-2011.)
Assertion
Ref Expression
3anan12  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ps  /\  ( ph  /\  ch ) ) )

Proof of Theorem 3anan12
StepHypRef Expression
1 3ancoma 941 . 2  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ps  /\  ph  /\ 
ch ) )
2 3anass 938 . 2  |-  ( ( ps  /\  ph  /\  ch )  <->  ( ps  /\  ( ph  /\  ch )
) )
31, 2bitri 240 1  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ps  /\  ( ph  /\  ch ) ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ wa 358    /\ w3a 934
This theorem is referenced by:  2reu5lem3  2972  fncnv  5314  dff1o2  5477  ixxun  10672  mreexexlem4d  13549  unocv  16580  iunocv  16581  mbfmax  19004  ulm2  19764  eqvinopb  24965  pridlnr  26661  bnj548  28929
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  df-3an 936
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