Theorem hbab1

Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by NM, 26-May-1993) (Proof shortened by Wolf Lammen, 25-Oct-2024)

	Ref	Expression
Assertion	hbab1	⊢ ( 𝑦 ∈ { 𝑥 ∣ 𝜑 } → ∀ 𝑥 𝑦 ∈ { 𝑥 ∣ 𝜑 } )

Proof

Step	Hyp	Ref	Expression
1		nfsab1	⊢ Ⅎ 𝑥 𝑦 ∈ { 𝑥 ∣ 𝜑 }
2	1	nf5ri	⊢ ( 𝑦 ∈ { 𝑥 ∣ 𝜑 } → ∀ 𝑥 𝑦 ∈ { 𝑥 ∣ 𝜑 } )