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Metamath Proof Explorer
Theorem fdm
Description: The domain of a mapping. (Contributed by NM, 2-Aug-1994) (Proof
shortened by Wolf Lammen, 29-May-2024)
|
|
Ref |
Expression |
|
Assertion |
fdm |
⊢ ( 𝐹 : 𝐴 ⟶ 𝐵 → dom 𝐹 = 𝐴 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
ffn |
⊢ ( 𝐹 : 𝐴 ⟶ 𝐵 → 𝐹 Fn 𝐴 ) |
| 2 |
1
|
fndmd |
⊢ ( 𝐹 : 𝐴 ⟶ 𝐵 → dom 𝐹 = 𝐴 ) |