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Theorem eel3132 28897
Description: syl2an 465 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 465 . 2  |-  ( ( ( ph  /\  ps )  /\  ( th  /\  ps ) )  ->  et )
543impdir 1241 1  |-  ( (
ph  /\  th  /\  ps )  ->  et )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360    /\ w3a 937
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 179  df-an 362  df-3an 939
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