Theorem hbs1

Description: The setvar x is not free in [ y / x ] ph when x and y are distinct. (Contributed by NM, 26-May-1993)

	Ref	Expression
Assertion	hbs1	⊢ ( [ 𝑦 / 𝑥 ] 𝜑 → ∀ 𝑥 [ 𝑦 / 𝑥 ] 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		nfs1v	⊢ Ⅎ 𝑥 [ 𝑦 / 𝑥 ] 𝜑
2	1	nf5ri	⊢ ( [ 𝑦 / 𝑥 ] 𝜑 → ∀ 𝑥 [ 𝑦 / 𝑥 ] 𝜑 )