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	⊢ ¬ 𝜑
Assertion	bj-nnfnth	⊢ Ⅎ' 𝑥 𝜑

Proof

Step	Hyp	Ref	Expression
1		bj-nnfnth.1	⊢ ¬ 𝜑
2	1	bj-nnfth	⊢ Ⅎ' 𝑥 ¬ 𝜑
3		bj-nnfnt	⊢ ( Ⅎ' 𝑥 𝜑 ↔ Ⅎ' 𝑥 ¬ 𝜑 )
4	2 3	mpbir	⊢ Ⅎ' 𝑥 𝜑