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Theorem 3anrot 983
Description: Rotation law for triple conjunction. (Contributed by NM, 8-Apr-1994.)
Assertion
Ref Expression
3anrot  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ps  /\  ch  /\ 
ph ) )

Proof of Theorem 3anrot
StepHypRef Expression
1 ancom 266 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  <->  ( ( ps  /\  ch )  /\  ph ) )
2 3anass 982 . 2  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ph  /\  ( ps  /\  ch ) ) )
3 df-3an 980 . 2  |-  ( ( ps  /\  ch  /\  ph )  <->  ( ( ps 
/\  ch )  /\  ph ) )
41, 2, 33bitr4i 212 1  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ps  /\  ch  /\ 
ph ) )
Colors of variables: wff set class
Syntax hints:    /\ wa 104    <-> wb 105    /\ w3a 978
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117  df-3an 980
This theorem is referenced by:  3ancomb  986  3anrev  988  3simpc  996  caovlem2d  6057  nnmcan  6510  modmulconst  11797  srgrmhm  12970  xmetpsmet  13362  comet  13492  lgsdi  13931
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