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Theorem mp3an1i 1236
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 30 . . 3  |-  ( ( ps  /\  ch  /\  th )  ->  ( ph  ->  ta ) )
41, 3mp3an1 1230 . 2  |-  ( ( ch  /\  th )  ->  ( ph  ->  ta ) )
54com12 30 1  |-  ( ph  ->  ( ( ch  /\  th )  ->  ta )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 101    /\ w3a 896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by: (None)
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