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Theorem mpan2i 658
Description: An inference based on modus ponens. (Contributed by NM, 10-Apr-1994.) (Proof shortened by Wolf Lammen, 19-Nov-2012.)
Hypotheses
Ref Expression
mpan2i.1  |-  ch
mpan2i.2  |-  ( ph  ->  ( ( ps  /\  ch )  ->  th )
)
Assertion
Ref Expression
mpan2i  |-  ( ph  ->  ( ps  ->  th )
)

Proof of Theorem mpan2i
StepHypRef Expression
1 mpan2i.1 . . 3  |-  ch
21a1i 10 . 2  |-  ( ph  ->  ch )
3 mpan2i.2 . 2  |-  ( ph  ->  ( ( ps  /\  ch )  ->  th )
)
42, 3mpan2d 655 1  |-  ( ph  ->  ( ps  ->  th )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  tcwf  7553  cflecard  7879  sqrlem7  11734  setciso  13923  lsmss1  14975  sincosq1lem  19865  pjcompi  22251  mdsl1i  22901  dfon2lem3  24141  dfon2lem7  24145  ismrc  26776
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
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