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Theorem eel3132 28493
Description: syl2an 463 with antecedents in standard conjunction form. (Contributed by Alan Sare, 27-Aug-2016.)
Hypotheses
Ref Expression
eel3132.1  |-  ( (
ph  /\  ps )  ->  ch )
eel3132.2  |-  ( ( th  /\  ps )  ->  ta )
eel3132.3  |-  ( ( ch  /\  ta )  ->  et )
Assertion
Ref Expression
eel3132  |-  ( (
ph  /\  th  /\  ps )  ->  et )

Proof of Theorem eel3132
StepHypRef Expression
1 eel3132.1 . . 3  |-  ( (
ph  /\  ps )  ->  ch )
2 eel3132.2 . . 3  |-  ( ( th  /\  ps )  ->  ta )
3 eel3132.3 . . 3  |-  ( ( ch  /\  ta )  ->  et )
41, 2, 3syl2an 463 . 2  |-  ( ( ( ph  /\  ps )  /\  ( th  /\  ps ) )  ->  et )
543impdir 1238 1  |-  ( (
ph  /\  th  /\  ps )  ->  et )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    /\ w3a 934
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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