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Theorem mp3an12i 1247
Description: mp3an 1243 with antecedents in standard conjunction form and with one hypothesis an implication. (Contributed by Alan Sare, 28-Aug-2016.)
Hypotheses
Ref Expression
mp3an12i.1  |-  ph
mp3an12i.2  |-  ps
mp3an12i.3  |-  ( ch 
->  th )
mp3an12i.4  |-  ( (
ph  /\  ps  /\  th )  ->  ta )
Assertion
Ref Expression
mp3an12i  |-  ( ch 
->  ta )

Proof of Theorem mp3an12i
StepHypRef Expression
1 mp3an12i.3 . 2  |-  ( ch 
->  th )
2 mp3an12i.1 . . 3  |-  ph
3 mp3an12i.2 . . 3  |-  ps
4 mp3an12i.4 . . 3  |-  ( (
ph  /\  ps  /\  th )  ->  ta )
52, 3, 4mp3an12 1233 . 2  |-  ( th 
->  ta )
61, 5syl 14 1  |-  ( ch 
->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by:  oddp1d2  10202
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