Theorem rabbieq

Description: Equivalent wff's correspond to restricted class abstractions which are equal with the same class. (Contributed by Peter Mazsa, 8-Jul-2019)

	Ref	Expression
Hypotheses	rabbieq.1	$$⊢B=\left\{x\in A|\phi \right\}$$
	rabbieq.2	$$⊢\phi \leftrightarrow \psi$$
Assertion	rabbieq	$$⊢B=\left\{x\in A|\psi \right\}$$

Proof

Step	Hyp	Ref	Expression
1		rabbieq.1	$$⊢B=\left\{x\in A|\phi \right\}$$
2		rabbieq.2	$$⊢\phi \leftrightarrow \psi$$
3	2	rabbii	$$⊢\left\{x\in A|\phi \right\}=\left\{x\in A|\psi \right\}$$
4	1 3	eqtri	$$⊢B=\left\{x\in A|\psi \right\}$$