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Theorem 3anan32 946
Description: Convert triple conjunction to conjunction, then commute. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)
Assertion
Ref Expression
3anan32  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ( ph  /\  ch )  /\  ps )
)

Proof of Theorem 3anan32
StepHypRef Expression
1 df-3an 936 . 2  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ( ph  /\  ps )  /\  ch )
)
2 an32 773 . 2  |-  ( ( ( ph  /\  ps )  /\  ch )  <->  ( ( ph  /\  ch )  /\  ps ) )
31, 2bitri 240 1  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ( ph  /\  ch )  /\  ps )
)
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ wa 358    /\ w3a 934
This theorem is referenced by:  dff1o3  5478  tz7.49c  6458  ispos2  14082  lbsacsbs  15909  obslbs  16630  leordtvallem1  16940  trfbas2  17538  lssbn  18773  sineq0  19889  dchrelbas3  20477  elicoelioo  23271  cndprobprob  23641  elno3  24309  ellimits  24450  dfdir2  25291  islbs4  27302  bnj543  28925
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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