ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  mpan2i Unicode version

Theorem mpan2i 407
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 9 . 2  |-  ( ph  ->  ch )
3 mpan2i.2 . 2  |-  ( ph  ->  ( ( ps  /\  ch )  ->  th )
)
42, 3mpan2d 404 1  |-  ( ph  ->  ( ps  ->  th )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 97
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 101
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator