Theorem rabssab

Description: A restricted class is a subclass of the corresponding unrestricted class. (Contributed by Mario Carneiro, 23-Dec-2016)

	Ref	Expression
Assertion	rabssab	$$⊢\left\{x\in A|\phi \right\}\subseteq \left\{x|\phi \right\}$$

Proof

Step	Hyp	Ref	Expression
1		df-rab	$$⊢\left\{x\in A|\phi \right\}=\left\{x|\left(x\in A\wedge \phi \right)\right\}$$
2		simpr	$$⊢\left(x\in A\wedge \phi \right)\to \phi$$
3	2	ss2abi	$$⊢\left\{x|\left(x\in A\wedge \phi \right)\right\}\subseteq \left\{x|\phi \right\}$$
4	1 3	eqsstri	$$⊢\left\{x\in A|\phi \right\}\subseteq \left\{x|\phi \right\}$$