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Theorem anandi3r 980
Description: Distribution of triple conjunction over conjunction. (Contributed by David A. Wheeler, 4-Nov-2018.)
Assertion
Ref Expression
anandi3r  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ( ph  /\  ps )  /\  ( ch  /\  ps ) ) )

Proof of Theorem anandi3r
StepHypRef Expression
1 3anan32 977 . 2  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ( ph  /\  ch )  /\  ps )
)
2 anandir 825 . 2  |-  ( ( ( ph  /\  ch )  /\  ps )  <->  ( ( ph  /\  ps )  /\  ( ch  /\  ps )
) )
31, 2bitri 249 1  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ( ph  /\  ps )  /\  ( ch  /\  ps ) ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    /\ wa 369    /\ w3a 965
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  df-3an 967
This theorem is referenced by:  alsi-no-surprise  31481
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