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Metamath Proof Explorer

Theorem dfqs2

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

		Ref	Expression
	Assertion	dfqs2	$⊢ A / R = ran (x \in A ⟼ [x] R)$

Step	Hyp	Ref	Expression
1		df-qs	$⊢ A / R = \{y \| \exists x \in A y = [x] R\}$
2		eqid	$⊢ (x \in A ⟼ [x] R) = (x \in A ⟼ [x] R)$
3	2	rnmpt	$⊢ ran (x \in A ⟼ [x] R) = \{y \| \exists x \in A y = [x] R\}$
4	1 3	eqtr4i	$⊢ A / R = ran (x \in A ⟼ [x] R)$