ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  sylan2d GIF version

Theorem sylan2d 282
Description: A syllogism deduction. (Contributed by NM, 15-Dec-2004.)
Hypotheses
Ref Expression
sylan2d.1 (𝜑 → (𝜓𝜒))
sylan2d.2 (𝜑 → ((𝜃𝜒) → 𝜏))
Assertion
Ref Expression
sylan2d (𝜑 → ((𝜃𝜓) → 𝜏))

Proof of Theorem sylan2d
StepHypRef Expression
1 sylan2d.1 . . 3 (𝜑 → (𝜓𝜒))
2 sylan2d.2 . . . 4 (𝜑 → ((𝜃𝜒) → 𝜏))
32ancomsd 260 . . 3 (𝜑 → ((𝜒𝜃) → 𝜏))
41, 3syland 281 . 2 (𝜑 → ((𝜓𝜃) → 𝜏))
54ancomsd 260 1 (𝜑 → ((𝜃𝜓) → 𝜏))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  syl2and  283  sylan2i  393  swopo  4071  prarloclemlo  6650  prodgt02  7894  prodge02  7896
  Copyright terms: Public domain W3C validator