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Metamath Proof Explorer

Theorem nftht

Description: Closed form of nfth . (Contributed by Wolf Lammen, 19-Aug-2018) (Proof shortened by BJ, 16-Sep-2021) (Proof shortened by Wolf Lammen, 3-Sep-2022)

		Ref	Expression
	Assertion	nftht	⊢ ( ∀ 𝑥 𝜑 → Ⅎ 𝑥 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		ax-1	⊢ ( ∀ 𝑥 𝜑 → ( ∃ 𝑥 𝜑 → ∀ 𝑥 𝜑 ) )
2	1	nfd	⊢ ( ∀ 𝑥 𝜑 → Ⅎ 𝑥 𝜑 )