Theorem efmndfv

Description: The function value of an endofunction. (Contributed by AV, 27-Jan-2024)

	Ref	Expression
Hypotheses	efmndbas.g	$$⊢G=\mathrm{EndoFMnd}\left(A\right)$$
	efmndbas.b	$$⊢B={\mathrm{Base}}_G$$
Assertion	efmndfv	$$⊢\left(F\in B\wedge X\in A\right)\to F\left(X\right)\in A$$

Proof

Step	Hyp	Ref	Expression
1		efmndbas.g	$$⊢G=\mathrm{EndoFMnd}\left(A\right)$$
2		efmndbas.b	$$⊢B={\mathrm{Base}}_G$$
3	1 2	efmndbasf	$$⊢F\in B\to F:A⟶A$$
4	3	ffvelcdmda	$$⊢\left(F\in B\wedge X\in A\right)\to F\left(X\right)\in A$$