Theorem efmndbasf

Description: Elements in the monoid of endofunctions on A are functions from A into itself. (Contributed by AV, 27-Jan-2024)

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

Proof

Step	Hyp	Ref	Expression
1		efmndbas.g	$$⊢G=\mathrm{EndoFMnd}\left(A\right)$$
2		efmndbas.b	$$⊢B={\mathrm{Base}}_G$$
3	1 2	elefmndbas2	$$⊢F\in B\to \left(F\in B\leftrightarrow F:A⟶A\right)$$
4	3	ibi	$$⊢F\in B\to F:A⟶A$$