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Theorem nf5dv 2012
 Description: Apply the definition of not-free in a context. (Contributed by Mario Carneiro, 11-Aug-2016.) df-nf 1701 changed. (Revised by Wolf Lammen, 18-Sep-2021.)
Hypothesis
Ref Expression
nf5dv.1 (𝜑 → (𝜓 → ∀𝑥𝜓))
Assertion
Ref Expression
nf5dv (𝜑 → Ⅎ𝑥𝜓)
Distinct variable group:   𝜑,𝑥
Allowed substitution hint:   𝜓(𝑥)

Proof of Theorem nf5dv
StepHypRef Expression
1 nf5dv.1 . . 3 (𝜑 → (𝜓 → ∀𝑥𝜓))
21alrimiv 1842 . 2 (𝜑 → ∀𝑥(𝜓 → ∀𝑥𝜓))
3 nf5-1 2010 . 2 (∀𝑥(𝜓 → ∀𝑥𝜓) → Ⅎ𝑥𝜓)
42, 3syl 17 1 (𝜑 → Ⅎ𝑥𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1473  Ⅎwnf 1699 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-10 2006 This theorem depends on definitions:  df-bi 196  df-ex 1696  df-nf 1701 This theorem is referenced by: (None)
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