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Theorem mp3anr1 1270
Description: An inference based on modus ponens. (Contributed by NM, 4-Nov-2006.)
Hypotheses
Ref Expression
mp3anr1.1  |-  ps
mp3anr1.2  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  th )
)  ->  ta )
Assertion
Ref Expression
mp3anr1  |-  ( (
ph  /\  ( ch  /\ 
th ) )  ->  ta )

Proof of Theorem mp3anr1
StepHypRef Expression
1 mp3anr1.1 . . 3  |-  ps
2 mp3anr1.2 . . . 4  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  th )
)  ->  ta )
32ancoms 264 . . 3  |-  ( ( ( ps  /\  ch  /\ 
th )  /\  ph )  ->  ta )
41, 3mp3anl1 1267 . 2  |-  ( ( ( ch  /\  th )  /\  ph )  ->  ta )
54ancoms 264 1  |-  ( (
ph  /\  ( ch  /\ 
th ) )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    /\ w3a 924
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 926
This theorem is referenced by: (None)
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