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Theorem eel012 28484
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
eel012.1  |-  ph
eel012.2  |-  ( ps 
->  ch )
eel012.3  |-  ( th 
->  ta )
eel012.4  |-  ( (
ph  /\  ch  /\  ta )  ->  et )
Assertion
Ref Expression
eel012  |-  ( ( ps  /\  th )  ->  et )

Proof of Theorem eel012
StepHypRef Expression
1 eel012.3 . 2  |-  ( th 
->  ta )
2 eel012.2 . . 3  |-  ( ps 
->  ch )
3 eel012.1 . . . 4  |-  ph
4 eel012.4 . . . 4  |-  ( (
ph  /\  ch  /\  ta )  ->  et )
53, 4mp3an1 1264 . . 3  |-  ( ( ch  /\  ta )  ->  et )
62, 5sylan 457 . 2  |-  ( ( ps  /\  ta )  ->  et )
71, 6sylan2 460 1  |-  ( ( ps  /\  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
  Copyright terms: Public domain W3C validator