Theorem bj-nfdt 36719

Description: Closed form of nf5d 2285 and nf5dh 2148. (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 36718	. 2 ⊢ (∀𝑥(𝜑 → (𝜓 → ∀𝑥𝜓)) → (∀𝑥𝜑 → Ⅎ𝑥𝜓))
2	1	imim2d 57	1 ⊢ (∀𝑥(𝜑 → (𝜓 → ∀𝑥𝜓)) → ((𝜑 → ∀𝑥𝜑) → (𝜑 → Ⅎ𝑥𝜓)))

Syntax hints:   → wi 4  ∀wal 1538  Ⅎwnf 1783

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-10 2142  ax-12 2178

This theorem depends on definitions:  df-bi 207  df-or 848  df-ex 1780  df-nf 1784

This theorem is referenced by: (None)