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Metamath Proof Explorer

Theorem bj-nnfth

Description: A variable is nonfree in a theorem, inference form. (Contributed by BJ, 28-Jul-2023)

		Ref	Expression
	Hypothesis	bj-nnfth.1	$⊢ φ$
	Assertion	bj-nnfth	$⊢ Ⅎ' x φ$

Step	Hyp	Ref	Expression
1		bj-nnfth.1	$⊢ φ$
2		bj-nnftht	$⊢ (φ \land \forall x φ) \to Ⅎ' x φ$
3	1 2	bj-mpgs	$⊢ Ⅎ' x φ$