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Theorem anandir 556
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 388 . . 3  |-  ( ( ch  /\  ch )  <->  ch )
21anbi2i 445 . 2  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  ch ) )  <->  ( ( ph  /\  ps )  /\  ch ) )
3 an4 551 . 2  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  ch ) )  <->  ( ( ph  /\  ch )  /\  ( ps  /\  ch )
) )
42, 3bitr3i 184 1  |-  ( ( ( ph  /\  ps )  /\  ch )  <->  ( ( ph  /\  ch )  /\  ( ps  /\  ch )
) )
Colors of variables: wff set class
Syntax hints:    /\ wa 102    <-> wb 103
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
This theorem is referenced by:  anandi3r  934  fununi  4998  imadiflem  5009  imadif  5010  imainlem  5011  elfzuzb  9115
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