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Theorem mpan2i 677
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 674 1  |-  ( ph  ->  ( ps  ->  th )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369
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 185  df-an 371
This theorem is referenced by:  tcwf  8290  cflecard  8622  sqrlem7  13032  setciso  15265  lsmss1  16473  sincosq1lem  22616  pjcompi  26252  mdsl1i  26902  dfon2lem3  28780  dfon2lem7  28784  tan2h  29611  dvasin  29667  ismrc  30224
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