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Theorem eel121 32986
Description: syl2an 477 with antecedents in standard conjunction form. (Contributed by Alan Sare, 27-Aug-2016.)
Hypotheses
Ref Expression
eel121.1  |-  ( ph  ->  ps )
eel121.2  |-  ( (
ph  /\  ch )  ->  th )
eel121.3  |-  ( ( ps  /\  th )  ->  ta )
Assertion
Ref Expression
eel121  |-  ( (
ph  /\  ch )  ->  ta )

Proof of Theorem eel121
StepHypRef Expression
1 eel121.1 . . 3  |-  ( ph  ->  ps )
2 eel121.2 . . 3  |-  ( (
ph  /\  ch )  ->  th )
3 eel121.3 . . 3  |-  ( ( ps  /\  th )  ->  ta )
41, 2, 3syl2an 477 . 2  |-  ( (
ph  /\  ( ph  /\ 
ch ) )  ->  ta )
54anabss5 814 1  |-  ( (
ph  /\  ch )  ->  ta )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369
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 185  df-an 371
This theorem is referenced by:  ax6e2ndeqALT  33212  sineq0ALT  33218
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