Theorem rabelpw

Description: A restricted class abstraction is an element of the power set of its restricting set. (Contributed by AV, 9-Oct-2023)

	Ref	Expression
Assertion	rabelpw	$$⊢A\in V\to \left\{x\in A|\phi \right\}\in 𝒫A$$

Proof

Step	Hyp	Ref	Expression
1		ssrab2	$$⊢\left\{x\in A|\phi \right\}\subseteq A$$
2		elpw2g	$$⊢A\in V\to \left(\left\{x\in A|\phi \right\}\in 𝒫A\leftrightarrow \left\{x\in A|\phi \right\}\subseteq A\right)$$
3	1 2	mpbiri	$$⊢A\in V\to \left\{x\in A|\phi \right\}\in 𝒫A$$