Theorem funfv2

Description: The value of a function. Definition of function value in Enderton p. 43. (Contributed by NM, 22-May-1998)

	Ref	Expression
Assertion	funfv2	|- ( Fun F -> ( F ` A ) = U. { y | A F y } )

Proof

Step	Hyp	Ref	Expression
1		funfv	|- ( Fun F -> ( F ` A ) = U. ( F " { A } ) )
2		funrel	|- ( Fun F -> Rel F )
3		relimasn	|- ( Rel F -> ( F " { A } ) = { y | A F y } )
4	2 3	syl	|- ( Fun F -> ( F " { A } ) = { y | A F y } )
5	4	unieqd	|- ( Fun F -> U. ( F " { A } ) = U. { y | A F y } )
6	1 5	eqtrd	|- ( Fun F -> ( F ` A ) = U. { y | A F y } )