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Theorem mp3an1i 1270
Description: An inference based on modus ponens. (Contributed by NM, 5-Jul-2005.)
Hypotheses
Ref Expression
mp3an1i.1  |-  ps
mp3an1i.2  |-  ( ph  ->  ( ( ps  /\  ch  /\  th )  ->  ta ) )
Assertion
Ref Expression
mp3an1i  |-  ( ph  ->  ( ( ch  /\  th )  ->  ta )
)

Proof of Theorem mp3an1i
StepHypRef Expression
1 mp3an1i.1 . . 3  |-  ps
2 mp3an1i.2 . . . 4  |-  ( ph  ->  ( ( ps  /\  ch  /\  th )  ->  ta ) )
32com12 27 . . 3  |-  ( ( ps  /\  ch  /\  th )  ->  ( ph  ->  ta ) )
41, 3mp3an1 1264 . 2  |-  ( ( ch  /\  th )  ->  ( ph  ->  ta ) )
54com12 27 1  |-  ( ph  ->  ( ( ch  /\  th )  ->  ta )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    /\ w3a 934
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