Metamath Proof Explorer
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 ) |