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Theorem mp3anl1 1274
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 425 . . 3  |-  ( (
ph  /\  ps  /\  ch )  ->  ( th  ->  ta ) )
41, 3mp3an1 1267 . 2  |-  ( ( ps  /\  ch )  ->  ( th  ->  ta ) )
54imp 420 1  |-  ( ( ( ps  /\  ch )  /\  th )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360    /\ w3a 937
This theorem is referenced by:  mp3anr1  1277  facavg  11593  iddvds  12864  blometi  22305  mdslmd3i  23836  atcvat2i  23891  chirredlem3  23896  mdsymlem1  23907
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 179  df-an 362  df-3an 939
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