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Metamath Proof Explorer

Theorem dfqs3

Description: Alternate definition of quotient set. (Contributed by Steven Nguyen, 7-Jun-2023)

		Ref	Expression
	Assertion	dfqs3	$⊢ A / R = ⋃_{x \in A} \{[x] R\}$

Step	Hyp	Ref	Expression
1		df-qs	$⊢ A / R = \{y \| \exists x \in A y = [x] R\}$
2		iunsn	$⊢ ⋃_{x \in A} \{[x] R\} = \{y \| \exists x \in A y = [x] R\}$
3	1 2	eqtr4i	$⊢ A / R = ⋃_{x \in A} \{[x] R\}$