ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  imp4a GIF version

Theorem imp4a 331
Description: An importation inference. (Contributed by NM, 26-Apr-1994.)
Hypothesis
Ref Expression
imp4.1 (φ → (ψ → (χ → (θτ))))
Assertion
Ref Expression
imp4a (φ → (ψ → ((χ θ) → τ)))

Proof of Theorem imp4a
StepHypRef Expression
1 imp4.1 . 2 (φ → (ψ → (χ → (θτ))))
2 impexp 250 . 2 (((χ θ) → τ) ↔ (χ → (θτ)))
31, 2syl6ibr 151 1 (φ → (ψ → ((χ θ) → τ)))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  imp4b  332  imp4d  334  imp55  343  imp511  344  equs5or  1708  reuss2  3211  tfrlem9  5876
  Copyright terms: Public domain W3C validator