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| Mirrors > Home > MPE Home > Th. List > f1ofo | Structured version Visualization version GIF version | ||
| Description: A one-to-one onto function is an onto function. (Contributed by NM, 28-Apr-2004.) |
| Ref | Expression |
|---|---|
| f1ofo | ⊢ (𝐹:𝐴–1-1-onto→𝐵 → 𝐹:𝐴–onto→𝐵) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | dff1o3 6854 | . 2 ⊢ (𝐹:𝐴–1-1-onto→𝐵 ↔ (𝐹:𝐴–onto→𝐵 ∧ Fun ◡𝐹)) | |
| 2 | 1 | simplbi 497 | 1 ⊢ (𝐹:𝐴–1-1-onto→𝐵 → 𝐹:𝐴–onto→𝐵) |
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