| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > rneqi | Structured version Visualization version GIF version | ||
| Description: Equality inference for range. (Contributed by NM, 4-Mar-2004.) |
| Ref | Expression |
|---|---|
| rneqi.1 | ⊢ 𝐴 = 𝐵 |
| Ref | Expression |
|---|---|
| rneqi | ⊢ ran 𝐴 = ran 𝐵 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | rneqi.1 | . 2 ⊢ 𝐴 = 𝐵 | |
| 2 | rneq 5947 | . 2 ⊢ (𝐴 = 𝐵 → ran 𝐴 = ran 𝐵) | |
| 3 | 1, 2 | ax-mp 5 | 1 ⊢ ran 𝐴 = ran 𝐵 |
| Copyright terms: Public domain | W3C validator |