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

Proof

Step	Hyp	Ref	Expression
1		bj-nnfth.1	$$⊢\phi$$
2		bj-nnftht	$$⊢\left(\phi \wedge \forall x\phi \right)\to Ⅎ\text{'}x\phi$$
3	1 2	bj-mpgs	$$⊢Ⅎ\text{'}x\phi$$