Theorem eqrabi

Description: Class element of a restricted class abstraction. (Contributed by Peter Mazsa, 24-Jul-2021)

	Ref	Expression
Hypothesis	eqrabi.1	$$⊢x\in A\leftrightarrow \left(x\in B\wedge \phi \right)$$
Assertion	eqrabi	$$⊢A=\left\{x\in B|\phi \right\}$$

Proof

Step	Hyp	Ref	Expression
1		eqrabi.1	$$⊢x\in A\leftrightarrow \left(x\in B\wedge \phi \right)$$
2	1	eqabi	$$⊢A=\left\{x|\left(x\in B\wedge \phi \right)\right\}$$
3		df-rab	$$⊢\left\{x\in B|\phi \right\}=\left\{x|\left(x\in B\wedge \phi \right)\right\}$$
4	2 3	eqtr4i	$$⊢A=\left\{x\in B|\phi \right\}$$