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Metamath Proof Explorer

Theorem uniqsw

Description: The union of a quotient set. More restrictive antecedent; kept for backward compatibility; for new work, prefer uniqs . (Contributed by NM, 9-Dec-2008) (Proof shortened by AV, 25-Nov-2025)

		Ref	Expression
	Assertion	uniqsw	$⊢ R \in V \to ⋃ (A / R) = R [A]$

Proof

Step	Hyp	Ref	Expression
1		resexg	$⊢ R \in V \to {R ↾}_{A} \in V$
2		uniqs	$⊢ {R ↾}_{A} \in V \to ⋃ (A / R) = R [A]$
3	1 2	syl	$⊢ R \in V \to ⋃ (A / R) = R [A]$