| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > frn | Structured version Visualization version GIF version | ||
| Description: The range of a mapping. (Contributed by NM, 3-Aug-1994.) |
| Ref | Expression |
|---|---|
| frn | ⊢ (𝐹:𝐴⟶𝐵 → ran 𝐹 ⊆ 𝐵) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-f 6565 | . 2 ⊢ (𝐹:𝐴⟶𝐵 ↔ (𝐹 Fn 𝐴 ∧ ran 𝐹 ⊆ 𝐵)) | |
| 2 | 1 | simprbi 496 | 1 ⊢ (𝐹:𝐴⟶𝐵 → ran 𝐹 ⊆ 𝐵) |
| Copyright terms: Public domain | W3C validator |