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Theorem bj-nfdt0 33016
Description: A theorem close to a closed form of nf5d 2280 and nf5dh 2179. (Contributed by BJ, 2-May-2019.)
Assertion
Ref Expression
bj-nfdt0 (∀𝑥(𝜑 → (𝜓 → ∀𝑥𝜓)) → (∀𝑥𝜑 → Ⅎ𝑥𝜓))

Proof of Theorem bj-nfdt0
StepHypRef Expression
1 alim 1885 . 2 (∀𝑥(𝜑 → (𝜓 → ∀𝑥𝜓)) → (∀𝑥𝜑 → ∀𝑥(𝜓 → ∀𝑥𝜓)))
2 nf5 2278 . 2 (Ⅎ𝑥𝜓 ↔ ∀𝑥(𝜓 → ∀𝑥𝜓))
31, 2syl6ibr 242 1 (∀𝑥(𝜑 → (𝜓 → ∀𝑥𝜓)) → (∀𝑥𝜑 → Ⅎ𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1628  wnf 1855
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1990  ax-6 2056  ax-7 2092  ax-10 2173  ax-12 2202
This theorem depends on definitions:  df-bi 197  df-or 827  df-ex 1852  df-nf 1857
This theorem is referenced by:  bj-nfdt  33017
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