Theorem wfximgfd

Description: The value of a function on its domain is in the image of the function. (Contributed by Stanislas Polu, 9-Mar-2020)

	Ref	Expression
Hypotheses	wfximgfd.1	|- ( ph -> C e. A )
	wfximgfd.2	|- ( ph -> F : A --> B )
Assertion	wfximgfd	|- ( ph -> ( F ` C ) e. ( F " A ) )

Proof

Step	Hyp	Ref	Expression
1		wfximgfd.1	|- ( ph -> C e. A )
2		wfximgfd.2	|- ( ph -> F : A --> B )
3	2	ffnd	|- ( ph -> F Fn A )
4	3 1 1	fnfvimad	|- ( ph -> ( F ` C ) e. ( F " A ) )