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Theorem 3anrev 946
Description: Reversal law for triple conjunction. (Contributed by NM, 21-Apr-1994.)
Assertion
Ref Expression
3anrev  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ch  /\  ps  /\ 
ph ) )

Proof of Theorem 3anrev
StepHypRef Expression
1 3ancoma 942 . 2  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ps  /\  ph  /\ 
ch ) )
2 3anrot 940 . 2  |-  ( ( ch  /\  ps  /\  ph )  <->  ( ps  /\  ph 
/\  ch ) )
31, 2bitr4i 243 1  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ch  /\  ps  /\ 
ph ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ w3a 935
This theorem is referenced by:  3com13  1157  nnmcan  6774  odupos  14449  btwnswapid2  25383  colinbtwnle  25483  frgra3v  27837  uunT11p2  28335  uunT12p5  28341  uun2221p2  28352  bnj345  28503  bnj1098  28579
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 937
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