ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  imim12i Unicode version

Theorem imim12i 59
Description: Inference joining two implications. (Contributed by NM, 5-Aug-1993.) (Proof shortened by O'Cat, 29-Oct-2011.)
Hypotheses
Ref Expression
imim12i.1  |-  ( ph  ->  ps )
imim12i.2  |-  ( ch 
->  th )
Assertion
Ref Expression
imim12i  |-  ( ( ps  ->  ch )  ->  ( ph  ->  th )
)

Proof of Theorem imim12i
StepHypRef Expression
1 imim12i.1 . 2  |-  ( ph  ->  ps )
2 imim12i.2 . . 3  |-  ( ch 
->  th )
32imim2i 12 . 2  |-  ( ( ps  ->  ch )  ->  ( ps  ->  th )
)
41, 3syl5 32 1  |-  ( ( ps  ->  ch )  ->  ( ph  ->  th )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by:  imim1i  60  hbim  1538  19.38  1669  cbvexdh  1919  exmoeudc  2082  bj-bdfindis  13904
  Copyright terms: Public domain W3C validator