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Metamath Proof Explorer

Theorem bj-nnfnth

Description: A variable is nonfree in the negation of a theorem, inference form. (Contributed by BJ, 27-Aug-2023)

		Ref	Expression
	Hypothesis	bj-nnfnth.1	$⊢ \neg φ$
	Assertion	bj-nnfnth	$⊢ Ⅎ' x φ$

Step	Hyp	Ref	Expression
1		bj-nnfnth.1	$⊢ \neg φ$
2	1	bj-nnfth	$⊢ Ⅎ' x \neg φ$
3		bj-nnfnt	$⊢ Ⅎ' x φ \leftrightarrow Ⅎ' x \neg φ$
4	2 3	mpbir	$⊢ Ⅎ' x φ$