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Theorem mp3an13 1234
Description: An inference based on modus ponens. (Contributed by NM, 14-Jul-2005.)
Hypotheses
Ref Expression
mp3an13.1  |-  ph
mp3an13.2  |-  ch
mp3an13.3  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
Assertion
Ref Expression
mp3an13  |-  ( ps 
->  th )

Proof of Theorem mp3an13
StepHypRef Expression
1 mp3an13.1 . 2  |-  ph
2 mp3an13.2 . . 3  |-  ch
3 mp3an13.3 . . 3  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
42, 3mp3an3 1232 . 2  |-  ( (
ph  /\  ps )  ->  th )
51, 4mpan 408 1  |-  ( ps 
->  th )
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:  pitonnlem1p1  6980  mulid1  7082  addltmul  8218  eluzaddi  8595  fz01en  9019  fznatpl1  9040  expubnd  9477  bernneq  9537  bernneq2  9538  dvds0  10123  odd2np1  10184  opoe  10207
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