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Theorem eel011 28482
Description: mp3an 1277 with antecedents in standard conjunction form and with two hypotheses which are implications. (Contributed by Alan Sare, 28-Aug-2016.)
Hypotheses
Ref Expression
eel011.1  |-  ph
eel011.2  |-  ( ps 
->  ch )
eel011.3  |-  ( ps 
->  th )
eel011.4  |-  ( (
ph  /\  ch  /\  th )  ->  ta )
Assertion
Ref Expression
eel011  |-  ( ps 
->  ta )

Proof of Theorem eel011
StepHypRef Expression
1 eel011.3 . . 3  |-  ( ps 
->  th )
2 eel011.2 . . . 4  |-  ( ps 
->  ch )
3 eel011.1 . . . . 5  |-  ph
4 eel011.4 . . . . 5  |-  ( (
ph  /\  ch  /\  th )  ->  ta )
53, 4mp3an1 1264 . . . 4  |-  ( ( ch  /\  th )  ->  ta )
62, 5sylan 457 . . 3  |-  ( ( ps  /\  th )  ->  ta )
71, 6sylan2 460 . 2  |-  ( ( ps  /\  ps )  ->  ta )
87anidms 626 1  |-  ( ps 
->  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