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Theorem mpan2i 660
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 11 . 2  |-  ( ph  ->  ch )
3 mpan2i.2 . 2  |-  ( ph  ->  ( ( ps  /\  ch )  ->  th )
)
42, 3mpan2d 657 1  |-  ( ph  ->  ( ps  ->  th )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360
This theorem is referenced by:  tcwf  7812  cflecard  8138  sqrlem7  12059  setciso  14251  lsmss1  15303  sincosq1lem  20410  pjcompi  23179  mdsl1i  23829  dfon2lem3  25417  dfon2lem7  25421  tan2h  26252  ismrc  26769
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 179  df-an 362
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