Theorem bj-nfdt 37362

Description: Closed form of nf5d 2322 and nf5dh 2185. (Contributed by BJ, 2-May-2019.)

Assertion

Ref	Expression
bj-nfdt	⊢ (∀𝑥(𝜑 → (𝜓 → ∀𝑥𝜓)) → ((𝜑 → ∀𝑥𝜑) → (𝜑 → Ⅎ𝑥𝜓)))

Proof of Theorem bj-nfdt

Step	Hyp	Ref	Expression
1		bj-nfdt0 37361	. 2 ⊢ (∀𝑥(𝜑 → (𝜓 → ∀𝑥𝜓)) → (∀𝑥𝜑 → Ⅎ𝑥𝜓))
2	1	imim2d 58	1 ⊢ (∀𝑥(𝜑 → (𝜓 → ∀𝑥𝜓)) → ((𝜑 → ∀𝑥𝜑) → (𝜑 → Ⅎ𝑥𝜓)))

This proof depends on syntax axioms:   → wi 4  ∀wal 1568  Ⅎwnf 1816

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-10 2179  ax-12 2216

This proof depends on definitions:  df-bi 210  df-or 862  df-ex 1813  df-nf 1817

This theorem is used by: (None)