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Theorem nf5dv 2143
Description: Apply the definition of not-free in a context. (Contributed by Mario Carneiro, 11-Aug-2016.) df-nf 1776 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 1902 . 2 (𝜑 → ∀𝑥𝜑)
2 nf5dv.1 . 2 (𝜑 → (𝜓 → ∀𝑥𝜓))
31, 2nf5dh 2142 1 (𝜑 → Ⅎ𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1526  wnf 1775
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-10 2136
This theorem depends on definitions:  df-bi 208  df-ex 1772  df-nf 1776
This theorem is referenced by: (None)
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