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Theorem mp3an3an 1306
Description: mp3an 1300 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 1287 . 2  |-  ( ( ch  /\  ta )  ->  et )
61, 2, 5syl2an 287 1  |-  ( ( ps  /\  th )  ->  et )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    /\ w3a 947
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 949
This theorem is referenced by:  mp3an2ani  1307  mapdom1g  6709  xrminrpcl  11011  tgrest  12265  sincosq1eq  12847
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