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Metamath Proof Explorer

Theorem nfnth

Description: No variable is (effectively) free in a non-theorem. (Contributed by Mario Carneiro, 6-Dec-2016) df-nf changed. (Revised by Wolf Lammen, 12-Sep-2021)

		Ref	Expression
	Hypothesis	nfnth.1	⊢ ¬ 𝜑
	Assertion	nfnth	⊢ Ⅎ 𝑥 𝜑

Proof

Step	Hyp	Ref	Expression
1		nfnth.1	⊢ ¬ 𝜑
2		nfntht2	⊢ ( ∀ 𝑥 ¬ 𝜑 → Ⅎ 𝑥 𝜑 )
3	2 1	mpg	⊢ Ⅎ 𝑥 𝜑