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 = ( EndoFMnd ‘ 𝐴 )
	efmndbas.b	⊢ 𝐵 = ( Base ‘ 𝐺 )
Assertion	efmndbasf	⊢ ( 𝐹 ∈ 𝐵 → 𝐹 : 𝐴 ⟶ 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		efmndbas.g	⊢ 𝐺 = ( EndoFMnd ‘ 𝐴 )
2		efmndbas.b	⊢ 𝐵 = ( Base ‘ 𝐺 )
3	1 2	elefmndbas2	⊢ ( 𝐹 ∈ 𝐵 → ( 𝐹 ∈ 𝐵 ↔ 𝐹 : 𝐴 ⟶ 𝐴 ) )
4	3	ibi	⊢ ( 𝐹 ∈ 𝐵 → 𝐹 : 𝐴 ⟶ 𝐴 )