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Theorem nfdv 1800
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 1797 . 2 (𝜑 → ∀𝑥(𝜓 → ∀𝑥𝜓))
3 df-nf 1391 . 2 (Ⅎ𝑥𝜓 ↔ ∀𝑥(𝜓 → ∀𝑥𝜓))
42, 3sylibr 132 1 (𝜑 → Ⅎ𝑥𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1283  wnf 1390
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-17 1460
This theorem depends on definitions:  df-bi 115  df-nf 1391
This theorem is referenced by: (None)
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