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Theorem 3anan32 931
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 922 . 2  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ( ph  /\  ps )  /\  ch )
)
2 an32 527 . 2  |-  ( ( ( ph  /\  ps )  /\  ch )  <->  ( ( ph  /\  ch )  /\  ps ) )
31, 2bitri 182 1  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ( ph  /\  ch )  /\  ps )
)
Colors of variables: wff set class
Syntax hints:    /\ wa 102    <-> wb 103    /\ w3a 920
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 922
This theorem is referenced by:  anandi3r  934  dff1o3  5207
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