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Theorem mp3anr2 1277
Description: An inference based on modus ponens. (Contributed by NM, 24-Nov-2006.)
Hypotheses
Ref Expression
mp3anr2.1  |-  ch
mp3anr2.2  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  th )
)  ->  ta )
Assertion
Ref Expression
mp3anr2  |-  ( (
ph  /\  ( ps  /\ 
th ) )  ->  ta )

Proof of Theorem mp3anr2
StepHypRef Expression
1 mp3anr2.1 . . 3  |-  ch
2 mp3anr2.2 . . . 4  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  th )
)  ->  ta )
32ancoms 440 . . 3  |-  ( ( ( ps  /\  ch  /\ 
th )  /\  ph )  ->  ta )
41, 3mp3anl2 1274 . 2  |-  ( ( ( ps  /\  th )  /\  ph )  ->  ta )
54ancoms 440 1  |-  ( (
ph  /\  ( ps  /\ 
th ) )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359    /\ w3a 936
This theorem is referenced by:  mulgp1  14906  vcz  22039  nvmdi  22121
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 178  df-an 361  df-3an 938
  Copyright terms: Public domain W3C validator