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Theorem mp3anl1 1237
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 112 . . 3  |-  ( (
ph  /\  ps  /\  ch )  ->  ( th  ->  ta ) )
41, 3mp3an1 1230 . 2  |-  ( ( ps  /\  ch )  ->  ( th  ->  ta ) )
54imp 119 1  |-  ( ( ( ps  /\  ch )  /\  th )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 101    /\ 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:  mp3anr1  1240  archnqq  6573  facavg  9614  iddvds  10121
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