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Theorem eel011 28153
Description: mp3an 1279 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 eel011.2 . 2  |-  ( ps 
->  ch )
2 eel011.3 . 2  |-  ( ps 
->  th )
3 eel011.1 . . 3  |-  ph
4 eel011.4 . . 3  |-  ( (
ph  /\  ch  /\  th )  ->  ta )
53, 4mp3an1 1266 . 2  |-  ( ( ch  /\  th )  ->  ta )
61, 2, 5syl2anc 643 1  |-  ( ps 
->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 936
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 178  df-an 361  df-3an 938
  Copyright terms: Public domain W3C validator