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Theorem mp3anl2 1272
Description: An inference based on modus ponens. (Contributed by NM, 24-Feb-2005.)
Hypotheses
Ref Expression
mp3anl2.1  |-  ps
mp3anl2.2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th )  ->  ta )
Assertion
Ref Expression
mp3anl2  |-  ( ( ( ph  /\  ch )  /\  th )  ->  ta )

Proof of Theorem mp3anl2
StepHypRef Expression
1 mp3anl2.1 . . 3  |-  ps
2 mp3anl2.2 . . . 4  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th )  ->  ta )
32ex 423 . . 3  |-  ( (
ph  /\  ps  /\  ch )  ->  ( th  ->  ta ) )
41, 3mp3an2 1265 . 2  |-  ( (
ph  /\  ch )  ->  ( th  ->  ta ) )
54imp 418 1  |-  ( ( ( ph  /\  ch )  /\  th )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    /\ w3a 934
This theorem is referenced by:  mp3anr2  1275  1dvds  12559  bcs2  21777  nmopub2tALT  22505  nmfnleub2  22522  nmophmi  22627  nmopcoadji  22697  atordi  22980  mdsymlem5  23003
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
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