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Theorem 3anan12 975
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 970 . 2  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ps  /\  ph  /\ 
ch ) )
2 3anass 967 . 2  |-  ( ( ps  /\  ph  /\  ch )  <->  ( ps  /\  ( ph  /\  ch )
) )
31, 2bitri 183 1  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ps  /\  ( ph  /\  ch ) ) )
Colors of variables: wff set class
Syntax hints:    /\ wa 103    <-> wb 104    /\ w3a 963
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 965
This theorem is referenced by:  fncnv  5193  dff1o2  5376
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