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Metamath Proof Explorer

Theorem qsexg

Description: A quotient set exists. (Contributed by FL, 19-May-2007) (Revised by Mario Carneiro, 9-Jul-2014)

		Ref	Expression
	Assertion	qsexg	$⊢ A \in V \to A / R \in V$

Step	Hyp	Ref	Expression
1		df-qs	$⊢ A / R = \{y \| \exists x \in A y = [x] R\}$
2		abrexexg	$⊢ A \in V \to \{y \| \exists x \in A y = [x] R\} \in V$
3	1 2	eqeltrid	$⊢ A \in V \to A / R \in V$