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Theorem eel2221 28781
Description: Deduction related to syl3an 1224 with antecedents in standard conjunction form. (Contributed by Alan Sare, 31-Aug-2016.)
Hypotheses
Ref Expression
eel2221.1  |-  ( ph  ->  ps )
eel2221.2  |-  ( ph  ->  ch )
eel2221.3  |-  ( ( th  /\  ph )  ->  ta )
eel2221.4  |-  ( ( ps  /\  ch  /\  ta )  ->  et )
Assertion
Ref Expression
eel2221  |-  ( ( th  /\  ph )  ->  et )

Proof of Theorem eel2221
StepHypRef Expression
1 eel2221.3 . . 3  |-  ( ( th  /\  ph )  ->  ta )
2 eel2221.2 . . . . 5  |-  ( ph  ->  ch )
3 eel2221.1 . . . . . 6  |-  ( ph  ->  ps )
4 eel2221.4 . . . . . . 7  |-  ( ( ps  /\  ch  /\  ta )  ->  et )
543exp 1150 . . . . . 6  |-  ( ps 
->  ( ch  ->  ( ta  ->  et ) ) )
63, 5syl 15 . . . . 5  |-  ( ph  ->  ( ch  ->  ( ta  ->  et ) ) )
72, 6syl5com 26 . . . 4  |-  ( ph  ->  ( ph  ->  ( ta  ->  et ) ) )
87pm2.43i 43 . . 3  |-  ( ph  ->  ( ta  ->  et ) )
91, 8syl5 28 . 2  |-  ( ph  ->  ( ( th  /\  ph )  ->  et )
)
109anabsi7 792 1  |-  ( ( th  /\  ph )  ->  et )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    /\ w3a 934
This theorem is referenced by:  suctrALT4  29020
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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