Theorem bj-nfdt

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

	Ref	Expression
Assertion	bj-nfdt	⊢ ( ∀ 𝑥 ( 𝜑 → ( 𝜓 → ∀ 𝑥 𝜓 ) ) → ( ( 𝜑 → ∀ 𝑥 𝜑 ) → ( 𝜑 → Ⅎ 𝑥 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		bj-nfdt0	⊢ ( ∀ 𝑥 ( 𝜑 → ( 𝜓 → ∀ 𝑥 𝜓 ) ) → ( ∀ 𝑥 𝜑 → Ⅎ 𝑥 𝜓 ) )
2	1	imim2d	⊢ ( ∀ 𝑥 ( 𝜑 → ( 𝜓 → ∀ 𝑥 𝜓 ) ) → ( ( 𝜑 → ∀ 𝑥 𝜑 ) → ( 𝜑 → Ⅎ 𝑥 𝜓 ) ) )