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Theorem mp3anr2 1298
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 266 . . 3  |-  ( ( ( ps  /\  ch  /\ 
th )  /\  ph )  ->  ta )
41, 3mp3anl2 1295 . 2  |-  ( ( ( ps  /\  th )  /\  ph )  ->  ta )
54ancoms 266 1  |-  ( (
ph  /\  ( ps  /\ 
th ) )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    /\ w3a 947
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 949
This theorem is referenced by: (None)
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