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 e. dom F -> A e. dom ( F |` { A } ) )

Proof

Step	Hyp	Ref	Expression
1		snidg	|- ( A e. dom F -> A e. { A } )
2		dmressnsn	|- ( A e. dom F -> dom ( F |` { A } ) = { A } )
3	1 2	eleqtrrd	|- ( A e. dom F -> A e. dom ( F |` { A } ) )