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Theorem mp3an12i 1320
Description: mp3an 1316 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 1306 . 2  |-  ( th 
->  ta )
61, 5syl 14 1  |-  ( ch 
->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 963
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 965
This theorem is referenced by:  map1  6713  suplocsrlempr  7638  geo2lim  11316  oddp1d2  11621  bezoutlema  11721  bezoutlemb  11722  exmidunben  11973  ismet  12550  isxmet  12551  coseq0negpitopi  12963  cosq34lt1  12977  cos02pilt1  12978  logdivlti  13008
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