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Theorem and4com 25043
Description: A consequence of  /\ associativity in a triple conjunct. (Contributed by FL, 14-Jul-2007.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Assertion
Ref Expression
and4com  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  th )
)  <->  ( ( ph  /\ 
ps  /\  ch )  /\  th ) )

Proof of Theorem and4com
StepHypRef Expression
1 3anass 938 . . 3  |-  ( ( ps  /\  ch  /\  th )  <->  ( ps  /\  ( ch  /\  th )
) )
21anbi2i 675 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  th )
)  <->  ( ph  /\  ( ps  /\  ( ch  /\  th ) ) ) )
3 3anass 938 . 2  |-  ( (
ph  /\  ps  /\  ( ch  /\  th ) )  <-> 
( ph  /\  ( ps  /\  ( ch  /\  th ) ) ) )
4 and4as 25042 . 2  |-  ( (
ph  /\  ps  /\  ( ch  /\  th ) )  <-> 
( ( ph  /\  ps  /\  ch )  /\  th ) )
52, 3, 43bitr2i 264 1  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  th )
)  <->  ( ( ph  /\ 
ps  /\  ch )  /\  th ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ wa 358    /\ w3a 934
This theorem is referenced by:  eeeeanv  25047
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  df-3an 936
  Copyright terms: Public domain W3C validator