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Metamath Proof Explorer

Theorem nfth

Description: No variable is (effectively) free in a theorem. (Contributed by Mario Carneiro, 11-Aug-2016) df-nf changed. (Revised by Wolf Lammen, 12-Sep-2021)

		Ref	Expression
	Hypothesis	nfth.1	$⊢ φ$
	Assertion	nfth	$⊢ Ⅎ x φ$

Proof

Step	Hyp	Ref	Expression
1		nfth.1	$⊢ φ$
2		nftht	$⊢ \forall x φ \to Ⅎ x φ$
3	2 1	mpg	$⊢ Ⅎ x φ$