Theorem ssrab2f

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

	Ref	Expression
Hypothesis	ssrab2f.1	$$⊢\underset{\_}{Ⅎ}xA$$
Assertion	ssrab2f	$$⊢\left\{x\in A|\phi \right\}\subseteq A$$

Proof

Step	Hyp	Ref	Expression
1		ssrab2f.1	$$⊢\underset{\_}{Ⅎ}xA$$
2		nfrab1	$$⊢\underset{\_}{Ⅎ}x\left\{x\in A|\phi \right\}$$
3	2 1	dfss3f	$$⊢\left\{x\in A|\phi \right\}\subseteq A\leftrightarrow \forall x\in \left\{x\in A|\phi \right\}x\in A$$
4		rabidim1	$$⊢x\in \left\{x\in A|\phi \right\}\to x\in A$$
5	3 4	mprgbir	$$⊢\left\{x\in A|\phi \right\}\subseteq A$$