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Metamath Proof Explorer

Theorem elqsi

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

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

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