ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3imp1 GIF version

Theorem 3imp1 1202
Description: Importation to left triple conjunction. (Contributed by NM, 24-Feb-2005.)
Hypothesis
Ref Expression
3imp1.1 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
Assertion
Ref Expression
3imp1 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜏)

Proof of Theorem 3imp1
StepHypRef Expression
1 3imp1.1 . . 3 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
213imp 1176 . 2 ((𝜑𝜓𝜒) → (𝜃𝜏))
32imp 123 1 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜏)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 963
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106
This theorem depends on definitions:  df-bi 116  df-3an 965
This theorem is referenced by:  reupick2  3393  ledivge1le  9633  leexp1a  10474
  Copyright terms: Public domain W3C validator