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Theorem eel112 28477
Description: syl3an 1224 with antecedents in standard conjunction form. (Contributed by Alan Sare, 31-Aug-2016.)
Hypotheses
Ref Expression
eel112.1  |-  ( ph  ->  ps )
eel112.2  |-  ( ph  ->  ch )
eel112.3  |-  ( th 
->  ta )
eel112.4  |-  ( ( ps  /\  ch  /\  ta )  ->  et )
Assertion
Ref Expression
eel112  |-  ( (
ph  /\  th )  ->  et )

Proof of Theorem eel112
StepHypRef Expression
1 eel112.1 . . 3  |-  ( ph  ->  ps )
2 eel112.2 . . 3  |-  ( ph  ->  ch )
3 eel112.3 . . 3  |-  ( th 
->  ta )
4 eel112.4 . . 3  |-  ( ( ps  /\  ch  /\  ta )  ->  et )
51, 2, 3, 4syl3an 1224 . 2  |-  ( (
ph  /\  ph  /\  th )  ->  et )
653anidm12 1239 1  |-  ( (
ph  /\  th )  ->  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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