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Theorem nf5dv 2141
 Description: Apply the definition of not-free in a context. (Contributed by Mario Carneiro, 11-Aug-2016.) df-nf 1828 changed. (Revised by Wolf Lammen, 18-Sep-2021.) (Proof shortened by Wolf Lammen, 13-Jul-2022.)
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 ax-5 1953 . 2 (𝜑 → ∀𝑥𝜑)
2 nf5dv.1 . 2 (𝜑 → (𝜓 → ∀𝑥𝜓))
31, 2nf5dh 2140 1 (𝜑 → Ⅎ𝑥𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1599  Ⅎwnf 1827 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-10 2134 This theorem depends on definitions:  df-bi 199  df-ex 1824  df-nf 1828 This theorem is referenced by: (None)
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