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

Theorem imim12i 53
Description: Inference joining two implications. (Contributed by NM, 5-Aug-1993.) (Proof shortened by O'Cat, 29-Oct-2011.)
Hypotheses
Ref Expression
imim12i.1 (φψ)
imim12i.2 (χθ)
Assertion
Ref Expression
imim12i ((ψχ) → (φθ))

Proof of Theorem imim12i
StepHypRef Expression
1 imim12i.1 . 2 (φψ)
2 imim12i.2 . . 3 (χθ)
32imim2i 12 . 2 ((ψχ) → (ψθ))
41, 3syl5 28 1 ((ψχ) → (φθ))
Colors of variables: wff set class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7
This theorem is referenced by:  imim1i  54  hbim  1410  19.38  1539  cbvexdh  1774  exmoeudc  1936  bj-bdfindis  8331
  Copyright terms: Public domain W3C validator