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Theorem bj-nfdt 33015
Description: Closed form of nf5d 2266 and nf5dh 2176. (Contributed by BJ, 2-May-2019.)
Assertion
Ref Expression
bj-nfdt (∀𝑥(𝜑 → (𝜓 → ∀𝑥𝜓)) → ((𝜑 → ∀𝑥𝜑) → (𝜑 → Ⅎ𝑥𝜓)))

Proof of Theorem bj-nfdt
StepHypRef Expression
1 bj-nfdt0 33014 . 2 (∀𝑥(𝜑 → (𝜓 → ∀𝑥𝜓)) → (∀𝑥𝜑 → Ⅎ𝑥𝜓))
21imim2d 57 1 (∀𝑥(𝜑 → (𝜓 → ∀𝑥𝜓)) → ((𝜑 → ∀𝑥𝜑) → (𝜑 → Ⅎ𝑥𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1630  wnf 1857
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1989  ax-6 2055  ax-7 2091  ax-10 2169  ax-12 2197
This theorem depends on definitions:  df-bi 197  df-or 384  df-ex 1854  df-nf 1859
This theorem is referenced by: (None)
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