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Metamath Proof Explorer

Theorem eldmressnsn

Description: The element of the domain of a restriction to a singleton is the element of the singleton. (Contributed by Alexander van der Vekens, 2-Jul-2017)

		Ref	Expression
	Assertion	eldmressnsn	$⊢ A \in dom F \to A \in dom ({F ↾}_{\{A\}})$

Proof

Step	Hyp	Ref	Expression
1		snidg	$⊢ A \in dom F \to A \in \{A\}$
2		dmressnsn	$⊢ A \in dom F \to dom ({F ↾}_{\{A\}}) = \{A\}$
3	1 2	eleqtrrd	$⊢ A \in dom F \to A \in dom ({F ↾}_{\{A\}})$