Theorem ssrab2f

Description: Subclass relation for a restricted class. (Contributed by Glauco Siliprandi, 26-Jun-2021)

	Ref	Expression
Hypothesis	ssrab2f.1	⊢ Ⅎ 𝑥 𝐴
Assertion	ssrab2f	⊢ { 𝑥 ∈ 𝐴 ∣ 𝜑 } ⊆ 𝐴

Proof

Step	Hyp	Ref	Expression
1		ssrab2f.1	⊢ Ⅎ 𝑥 𝐴
2		nfrab1	⊢ Ⅎ 𝑥 { 𝑥 ∈ 𝐴 ∣ 𝜑 }
3	2 1	dfss3f	⊢ ( { 𝑥 ∈ 𝐴 ∣ 𝜑 } ⊆ 𝐴 ↔ ∀ 𝑥 ∈ { 𝑥 ∈ 𝐴 ∣ 𝜑 } 𝑥 ∈ 𝐴 )
4		rabidim1	⊢ ( 𝑥 ∈ { 𝑥 ∈ 𝐴 ∣ 𝜑 } → 𝑥 ∈ 𝐴 )
5	3 4	mprgbir	⊢ { 𝑥 ∈ 𝐴 ∣ 𝜑 } ⊆ 𝐴