Theorem eqriv

Description: Infer equality of classes from equivalence of membership. (Contributed by NM, 21-Jun-1993)

	Ref	Expression
Hypothesis	eqriv.1	$$⊢x\in A\leftrightarrow x\in B$$
Assertion	eqriv	$$⊢A=B$$

Proof

Step	Hyp	Ref	Expression
1		eqriv.1	$$⊢x\in A\leftrightarrow x\in B$$
2		dfcleq	$$⊢A=B\leftrightarrow \forall x\left(x\in A\leftrightarrow x\in B\right)$$
3	2 1	mpgbir	$$⊢A=B$$