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Theorem anandir 802
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 625 . . 3  |-  ( ( ch  /\  ch )  <->  ch )
21anbi2i 675 . 2  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  ch ) )  <->  ( ( ph  /\  ps )  /\  ch ) )
3 an4 797 . 2  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  ch ) )  <->  ( ( ph  /\  ch )  /\  ( ps  /\  ch )
) )
42, 3bitr3i 242 1  |-  ( ( ( ph  /\  ps )  /\  ch )  <->  ( ( ph  /\  ch )  /\  ( ps  /\  ch )
) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ wa 358
This theorem is referenced by:  cadan  1382  disjxun  4021  fununi  5316  imadif  5327  elfzuzb  10792  5oalem3  22235  5oalem5  22237  wfrlem5  24260  frrlem5  24285  frgra3v  28180  un2122  28565
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
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