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Theorem mp3anl3 1273
Description: An inference based on modus ponens. (Contributed by NM, 24-Feb-2005.)
Hypotheses
Ref Expression
mp3anl3.1  |-  ch
mp3anl3.2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th )  ->  ta )
Assertion
Ref Expression
mp3anl3  |-  ( ( ( ph  /\  ps )  /\  th )  ->  ta )

Proof of Theorem mp3anl3
StepHypRef Expression
1 mp3anl3.1 . . 3  |-  ch
2 mp3anl3.2 . . . 4  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th )  ->  ta )
32ex 423 . . 3  |-  ( (
ph  /\  ps  /\  ch )  ->  ( th  ->  ta ) )
41, 3mp3an3 1266 . 2  |-  ( (
ph  /\  ps )  ->  ( th  ->  ta ) )
54imp 418 1  |-  ( ( ( ph  /\  ps )  /\  th )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    /\ w3a 934
This theorem is referenced by:  mp3anr3  1276  ioombl  18938  nmopadjlem  22685  nmopcoadji  22697  atcvat3i  22992
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
  Copyright terms: Public domain W3C validator