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

Theorem sylani 403
Description: A syllogism inference. (Contributed by NM, 2-May-1996.)
Hypotheses
Ref Expression
sylani.1 (𝜑𝜒)
sylani.2 (𝜓 → ((𝜒𝜃) → 𝜏))
Assertion
Ref Expression
sylani (𝜓 → ((𝜑𝜃) → 𝜏))

Proof of Theorem sylani
StepHypRef Expression
1 sylani.1 . . 3 (𝜑𝜒)
21a1i 9 . 2 (𝜓 → (𝜑𝜒))
3 sylani.2 . 2 (𝜓 → ((𝜒𝜃) → 𝜏))
42, 3syland 291 1 (𝜓 → ((𝜑𝜃) → 𝜏))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem is referenced by:  syl2ani  405  fiintim  6785  lcmdvds  11687
  Copyright terms: Public domain W3C validator