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Theorem anandi3 976
Description: Distribution of triple conjunction over conjunction. (Contributed by David A. Wheeler, 4-Nov-2018.)
Assertion
Ref Expression
anandi3  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ( ph  /\  ps )  /\  ( ph  /\  ch ) ) )

Proof of Theorem anandi3
StepHypRef Expression
1 3anass 967 . 2  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ph  /\  ( ps  /\  ch ) ) )
2 anandi 580 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  <->  ( ( ph  /\  ps )  /\  ( ph  /\  ch )
) )
31, 2bitri 183 1  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ( ph  /\  ps )  /\  ( ph  /\  ch ) ) )
Colors of variables: wff set class
Syntax hints:    /\ wa 103    <-> wb 104    /\ w3a 963
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  df-3an 965
This theorem is referenced by: (None)
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