Theorem ecelqsi

Description: Membership of an equivalence class in a quotient set. (Contributed by NM, 25-Jul-1995) (Revised by Mario Carneiro, 9-Jul-2014)

	Ref	Expression
Hypothesis	ecelqsi.1	$$⊢R\in \mathrm{V}$$
Assertion	ecelqsi	$$⊢B\in A\to \left[B\right]R\in \left(A/R\right)$$

Proof

Step	Hyp	Ref	Expression
1		ecelqsi.1	$$⊢R\in \mathrm{V}$$
2		ecelqsw	$$⊢\left(R\in \mathrm{V}\wedge B\in A\right)\to \left[B\right]R\in \left(A/R\right)$$
3	1 2	mpan	$$⊢B\in A\to \left[B\right]R\in \left(A/R\right)$$