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 e. V -> U. ( A /. R ) = ( R " A ) )

Proof

Step	Hyp	Ref	Expression
1		resexg	|- ( R e. V -> ( R |` A ) e. _V )
2		uniqs	|- ( ( R |` A ) e. _V -> U. ( A /. R ) = ( R " A ) )
3	1 2	syl	|- ( R e. V -> U. ( A /. R ) = ( R " A ) )