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Theorem pm3.2an3 1131
Description: pm3.2 434 for a triple conjunction. (Contributed by Alan Sare, 24-Oct-2011.)
Assertion
Ref Expression
pm3.2an3  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( ph  /\  ps  /\  ch ) ) ) )

Proof of Theorem pm3.2an3
StepHypRef Expression
1 pm3.2 434 . . 3  |-  ( (
ph  /\  ps )  ->  ( ch  ->  (
( ph  /\  ps )  /\  ch ) ) )
21ex 423 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( ( ph  /\ 
ps )  /\  ch ) ) ) )
3 df-3an 936 . . 3  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ( ph  /\  ps )  /\  ch )
)
43bicomi 193 . 2  |-  ( ( ( ph  /\  ps )  /\  ch )  <->  ( ph  /\ 
ps  /\  ch )
)
52, 4syl8ib 222 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( ph  /\  ps  /\  ch ) ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    /\ w3a 934
This theorem is referenced by:  3exp  1150  intcont  25646  idsubfun  25961  tratrb  28598  19.21a3con13vVD  28944  tratrbVD  28953
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
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