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Theorem 3ancomb 971
Description: Commutation law for triple conjunction. (Contributed by NM, 21-Apr-1994.)
Assertion
Ref Expression
3ancomb  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ph  /\  ch  /\ 
ps ) )

Proof of Theorem 3ancomb
StepHypRef Expression
1 3ancoma 970 . 2  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ps  /\  ph  /\ 
ch ) )
2 3anrot 968 . 2  |-  ( ( ps  /\  ph  /\  ch )  <->  ( ph  /\  ch  /\  ps ) )
31, 2bitri 183 1  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ph  /\  ch  /\ 
ps ) )
Colors of variables: wff set class
Syntax hints:    <-> 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:  3simpb  980  addcanprg  7444  elioore  9721  xmetrtri  12575
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