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Theorem mp3an2i 1274
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
mp3an2i.1  |-  ph
mp3an2i.2  |-  ( ps 
->  ch )
mp3an2i.3  |-  ( ps 
->  th )
mp3an2i.4  |-  ( (
ph  /\  ch  /\  th )  ->  ta )
Assertion
Ref Expression
mp3an2i  |-  ( ps 
->  ta )

Proof of Theorem mp3an2i
StepHypRef Expression
1 mp3an2i.2 . 2  |-  ( ps 
->  ch )
2 mp3an2i.3 . 2  |-  ( ps 
->  th )
3 mp3an2i.1 . . 3  |-  ph
4 mp3an2i.4 . . 3  |-  ( (
ph  /\  ch  /\  th )  ->  ta )
53, 4mp3an1 1256 . 2  |-  ( ( ch  /\  th )  ->  ta )
61, 2, 5syl2anc 403 1  |-  ( ps 
->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ 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:  en2eleq  6511  nnledivrp  8907  frec2uzsucd  9472  gcdn0gt0  10502  divgcdodd  10655  sqpweven  10686  2sqpwodd  10687
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