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Theorem mp3anl1 1320
Description: An inference based on modus ponens. (Contributed by NM, 24-Feb-2005.)
Hypotheses
Ref Expression
mp3anl1.1  |-  ph
mp3anl1.2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th )  ->  ta )
Assertion
Ref Expression
mp3anl1  |-  ( ( ( ps  /\  ch )  /\  th )  ->  ta )

Proof of Theorem mp3anl1
StepHypRef Expression
1 mp3anl1.1 . . 3  |-  ph
2 mp3anl1.2 . . . 4  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th )  ->  ta )
32ex 432 . . 3  |-  ( (
ph  /\  ps  /\  ch )  ->  ( th  ->  ta ) )
41, 3mp3an1 1313 . 2  |-  ( ( ps  /\  ch )  ->  ( th  ->  ta ) )
54imp 427 1  |-  ( ( ( ps  /\  ch )  /\  th )  ->  ta )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 367    /\ w3a 974
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 369  df-3an 976
This theorem is referenced by:  mp3anr1  1323  facavg  12333  iddvds  14098  blometi  26012  mdslmd3i  27544  atcvat2i  27599  chirredlem3  27604  mdsymlem1  27615  isprm7  36021
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