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	$$⊢\phi \to C\in A$$
	wfximgfd.2	$$⊢\phi \to F:A⟶B$$
Assertion	wfximgfd	$$⊢\phi \to F\left(C\right)\in F\left[A\right]$$

Proof

Step	Hyp	Ref	Expression
1		wfximgfd.1	$$⊢\phi \to C\in A$$
2		wfximgfd.2	$$⊢\phi \to F:A⟶B$$
3	2	ffnd	$$⊢\phi \to FFnA$$
4	3 1 1	fnfvimad	$$⊢\phi \to F\left(C\right)\in F\left[A\right]$$