Theorem sbf2

Description: Substitution has no effect on a bound variable. (Contributed by NM, 1-Jul-2005)

	Ref	Expression
Assertion	sbf2	⊢ ( [ 𝑦 / 𝑥 ] ∀ 𝑥 𝜑 ↔ ∀ 𝑥 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		nfa1	⊢ Ⅎ 𝑥 ∀ 𝑥 𝜑
2	1	sbf	⊢ ( [ 𝑦 / 𝑥 ] ∀ 𝑥 𝜑 ↔ ∀ 𝑥 𝜑 )