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Metamath Proof Explorer
Theorem frn
Description: The range of a mapping. (Contributed by NM, 3-Aug-1994)
|
|
Ref |
Expression |
|
Assertion |
frn |
⊢ ( 𝐹 : 𝐴 ⟶ 𝐵 → ran 𝐹 ⊆ 𝐵 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
df-f |
⊢ ( 𝐹 : 𝐴 ⟶ 𝐵 ↔ ( 𝐹 Fn 𝐴 ∧ ran 𝐹 ⊆ 𝐵 ) ) |
| 2 |
1
|
simprbi |
⊢ ( 𝐹 : 𝐴 ⟶ 𝐵 → ran 𝐹 ⊆ 𝐵 ) |