Theorem bj-nnftht

Description: A variable is nonfree in a theorem. The antecedent is in the "strong necessity" modality of modal logic in order not to require sp (modal T), as in bj-nnfbi . (Contributed by BJ, 28-Jul-2023)

	Ref	Expression
Assertion	bj-nnftht	⊢ ( ( 𝜑 ∧ ∀ 𝑥 𝜑 ) → Ⅎ' 𝑥 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		bj-alnnf2	⊢ ( 𝜑 → ( ∀ 𝑥 𝜑 ↔ Ⅎ' 𝑥 𝜑 ) )
2	1	biimpa	⊢ ( ( 𝜑 ∧ ∀ 𝑥 𝜑 ) → Ⅎ' 𝑥 𝜑 )