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Theorem mp3an3an 1275
Description: mp3an 1269 with antecedents in standard conjunction form and with two hypotheses which are implications. (Contributed by Alan Sare, 28-Aug-2016.)
Hypotheses
Ref Expression
mp3an3an.1  |-  ph
mp3an3an.2  |-  ( ps 
->  ch )
mp3an3an.3  |-  ( th 
->  ta )
mp3an3an.4  |-  ( (
ph  /\  ch  /\  ta )  ->  et )
Assertion
Ref Expression
mp3an3an  |-  ( ( ps  /\  th )  ->  et )

Proof of Theorem mp3an3an
StepHypRef Expression
1 mp3an3an.2 . 2  |-  ( ps 
->  ch )
2 mp3an3an.3 . 2  |-  ( th 
->  ta )
3 mp3an3an.1 . . 3  |-  ph
4 mp3an3an.4 . . 3  |-  ( (
ph  /\  ch  /\  ta )  ->  et )
53, 4mp3an1 1256 . 2  |-  ( ( ch  /\  ta )  ->  et )
61, 2, 5syl2an 283 1  |-  ( ( ps  /\  th )  ->  et )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    /\ w3a 920
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 922
This theorem is referenced by:  mp3an2ani  1276
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