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Theorem mp3anr3 1276
Description: An inference based on modus ponens. (Contributed by NM, 19-Oct-2007.)
Hypotheses
Ref Expression
mp3anr3.1  |-  th
mp3anr3.2  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  th )
)  ->  ta )
Assertion
Ref Expression
mp3anr3  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  ta )

Proof of Theorem mp3anr3
StepHypRef Expression
1 mp3anr3.1 . . 3  |-  th
2 mp3anr3.2 . . . 4  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  th )
)  ->  ta )
32ancoms 439 . . 3  |-  ( ( ( ps  /\  ch  /\ 
th )  /\  ph )  ->  ta )
41, 3mp3anl3 1273 . 2  |-  ( ( ( ps  /\  ch )  /\  ph )  ->  ta )
54ancoms 439 1  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    /\ w3a 934
This theorem is referenced by:  splid  11468
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