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

Theorem mpisyl 1332
Description: A syllogism combined with a modus ponens inference. (Contributed by Alan Sare, 25-Jul-2011.)
Hypotheses
Ref Expression
mpisyl.1 (φψ)
mpisyl.2 χ
mpisyl.3 (ψ → (χθ))
Assertion
Ref Expression
mpisyl (φθ)

Proof of Theorem mpisyl
StepHypRef Expression
1 mpisyl.1 . 2 (φψ)
2 mpisyl.2 . . 3 χ
3 mpisyl.3 . . 3 (ψ → (χθ))
42, 3mpi 15 . 2 (ψθ)
51, 4syl 14 1 (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:  ceqsex  2586  reusv1  4156  fliftcnv  5378  fliftfun  5379  tfrlemibfn  5883
  Copyright terms: Public domain W3C validator