ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  imim12d Unicode version

Theorem imim12d 74
Description: Deduction combining antecedents and consequents. (Contributed by NM, 7-Aug-1994.) (Proof shortened by O'Cat, 30-Oct-2011.)
Hypotheses
Ref Expression
imim12d.1  |-  ( ph  ->  ( ps  ->  ch ) )
imim12d.2  |-  ( ph  ->  ( th  ->  ta ) )
Assertion
Ref Expression
imim12d  |-  ( ph  ->  ( ( ch  ->  th )  ->  ( ps  ->  ta ) ) )

Proof of Theorem imim12d
StepHypRef Expression
1 imim12d.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
2 imim12d.2 . . 3  |-  ( ph  ->  ( th  ->  ta ) )
32imim2d 54 . 2  |-  ( ph  ->  ( ( ch  ->  th )  ->  ( ch  ->  ta ) ) )
41, 3syl5d 68 1  |-  ( ph  ->  ( ( ch  ->  th )  ->  ( ps  ->  ta ) ) )
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:  imim1d  75  equveli  1717  hbsb4t  1966  mo23  2018  rspcimdv  2764  r19.29uz  10732  txlm  12375  metcnpi3  12613  addcncntoplem  12647  cnplimcim  12732  setindis  13092  bdsetindis  13094  bj-findis  13104
  Copyright terms: Public domain W3C validator