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Theorem 3anrev 976
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 972 . 2  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ps  /\  ph  /\ 
ch ) )
2 3anrot 970 . 2  |-  ( ( ch  /\  ps  /\  ph )  <->  ( ps  /\  ph 
/\  ch ) )
31, 2bitr4i 252 1  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ch  /\  ps  /\ 
ph ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    /\ w3a 965
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 967
This theorem is referenced by:  3com13  1193  an33rean  1333  nnmcan  7184  odupos  15425  pocnv  27719  btwnswapid2  28194  colinbtwnle  28294  frgra3v  30743  uunT11p2  31864  uunT12p5  31870  uun2221p2  31881  bnj345  32035  bnj1098  32110
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