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Theorem anandir 565
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 393 . . 3  |-  ( ( ch  /\  ch )  <->  ch )
21anbi2i 452 . 2  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  ch ) )  <->  ( ( ph  /\  ps )  /\  ch ) )
3 an4 560 . 2  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  ch ) )  <->  ( ( ph  /\  ch )  /\  ( ps  /\  ch )
) )
42, 3bitr3i 185 1  |-  ( ( ( ph  /\  ps )  /\  ch )  <->  ( ( ph  /\  ch )  /\  ( ps  /\  ch )
) )
Colors of variables: wff set class
Syntax hints:    /\ wa 103    <-> wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  anandi3r  961  fununi  5161  imadiflem  5172  imadif  5173  imainlem  5174  elfzuzb  9768
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