Theorem elqsi

Description: Membership in a quotient set. (Contributed by NM, 23-Jul-1995)

	Ref	Expression
Assertion	elqsi	$$⊢B\in \left(A/R\right)\to \exists x\in AB=\left[x\right]R$$

Proof

Step	Hyp	Ref	Expression
1		elqsg	$$⊢B\in \left(A/R\right)\to \left(B\in \left(A/R\right)\leftrightarrow \exists x\in AB=\left[x\right]R\right)$$
2	1	ibi	$$⊢B\in \left(A/R\right)\to \exists x\in AB=\left[x\right]R$$