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

Theorem nfdv 1757
Description: Apply the definition of not-free in a context. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfdv.1 (𝜑 → (𝜓 → ∀𝑥𝜓))
Assertion
Ref Expression
nfdv (𝜑 → Ⅎ𝑥𝜓)
Distinct variable group:   𝜑,𝑥
Allowed substitution hint:   𝜓(𝑥)

Proof of Theorem nfdv
StepHypRef Expression
1 nfdv.1 . . 3 (𝜑 → (𝜓 → ∀𝑥𝜓))
21alrimiv 1754 . 2 (𝜑 → ∀𝑥(𝜓 → ∀𝑥𝜓))
3 df-nf 1350 . 2 (Ⅎ𝑥𝜓 ↔ ∀𝑥(𝜓 → ∀𝑥𝜓))
42, 3sylibr 137 1 (𝜑 → Ⅎ𝑥𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1241  wnf 1349
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-17 1419
This theorem depends on definitions:  df-bi 110  df-nf 1350
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator