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Theorem eel001 28487
Description: mp3an 1277 with antecedents in standard conjunction form and with one hypothesis an implication. (Contributed by Alan Sare, 28-Aug-2016.)
Hypotheses
Ref Expression
eel001.1  |-  ph
eel001.2  |-  ps
eel001.3  |-  ( ch 
->  th )
eel001.4  |-  ( (
ph  /\  ps  /\  th )  ->  ta )
Assertion
Ref Expression
eel001  |-  ( ch 
->  ta )

Proof of Theorem eel001
StepHypRef Expression
1 eel001.3 . 2  |-  ( ch 
->  th )
2 eel001.2 . . 3  |-  ps
3 eel001.1 . . . 4  |-  ph
4 eel001.4 . . . 4  |-  ( (
ph  /\  ps  /\  th )  ->  ta )
53, 4mp3an1 1264 . . 3  |-  ( ( ps  /\  th )  ->  ta )
62, 5mpan 651 . 2  |-  ( th 
->  ta )
71, 6syl 15 1  |-  ( ch 
->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ 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
  Copyright terms: Public domain W3C validator