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Theorem anandir 827
Description: Distribution of conjunction over conjunction. (Contributed by NM, 24-Aug-1995.)
Assertion
Ref Expression
anandir  |-  ( ( ( ph  /\  ps )  /\  ch )  <->  ( ( ph  /\  ch )  /\  ( ps  /\  ch )
) )

Proof of Theorem anandir
StepHypRef Expression
1 anidm 644 . . 3  |-  ( ( ch  /\  ch )  <->  ch )
21anbi2i 694 . 2  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  ch ) )  <->  ( ( ph  /\  ps )  /\  ch ) )
3 an4 822 . 2  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  ch ) )  <->  ( ( ph  /\  ch )  /\  ( ps  /\  ch )
) )
42, 3bitr3i 251 1  |-  ( ( ( ph  /\  ps )  /\  ch )  <->  ( ( ph  /\  ch )  /\  ( ps  /\  ch )
) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    /\ wa 369
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
This theorem is referenced by:  anandi3r  988  cadanOLD  1444  disjxun  4451  fununi  5660  imadif  5669  elfzuzb  11694  frgra3v  24825  5oalem3  26397  5oalem5  26399  wfrlem5  29274  frrlem5  29318  nzin  31147  un2122  33068
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