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	$$⊢\neg \phi$$
Assertion	bj-nnfnth	$$⊢Ⅎ\text{'}x\phi$$

Proof

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