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Theorem 3ancoma 929
Description: Commutation law for triple conjunction. (Contributed by NM, 21-Apr-1994.)
Assertion
Ref Expression
3ancoma  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ps  /\  ph  /\ 
ch ) )

Proof of Theorem 3ancoma
StepHypRef Expression
1 ancom 262 . . 3  |-  ( (
ph  /\  ps )  <->  ( ps  /\  ph )
)
21anbi1i 446 . 2  |-  ( ( ( ph  /\  ps )  /\  ch )  <->  ( ( ps  /\  ph )  /\  ch ) )
3 df-3an 924 . 2  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ( ph  /\  ps )  /\  ch )
)
4 df-3an 924 . 2  |-  ( ( ps  /\  ph  /\  ch )  <->  ( ( ps 
/\  ph )  /\  ch ) )
52, 3, 43bitr4i 210 1  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ps  /\  ph  /\ 
ch ) )
Colors of variables: wff set class
Syntax hints:    /\ wa 102    <-> wb 103    /\ w3a 922
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 924
This theorem is referenced by:  3ancomb  930  3anrev  932  3anan12  934  3com12  1145  elfzmlbp  9464  elfzo2  9482
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