Theorem bj-alnnf2

Description: If a proposition holds, then it holds for all values of a given variable if and only if it does not depend on that variable. (Contributed by BJ, 28-Mar-2026)

	Ref	Expression
Assertion	bj-alnnf2	⊢ ( 𝜑 → ( ∀ 𝑥 𝜑 ↔ Ⅎ' 𝑥 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		bj-alnnf	⊢ ( ( 𝜑 → ∀ 𝑥 𝜑 ) ↔ ( 𝜑 → Ⅎ' 𝑥 𝜑 ) )
2	1	pm5.74ri	⊢ ( 𝜑 → ( ∀ 𝑥 𝜑 ↔ Ⅎ' 𝑥 𝜑 ) )