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| Mirrors > Home > MPE Home > Th. List > zringbas | Structured version Visualization version GIF version | ||
| Description: The integers are the base of the ring of integers. (Contributed by Thierry Arnoux, 31-Oct-2017.) (Revised by AV, 9-Jun-2019.) |
| Ref | Expression |
|---|---|
| zringbas | ⊢ ℤ = (Base‘ℤring) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | zsscn 12621 | . 2 ⊢ ℤ ⊆ ℂ | |
| 2 | df-zring 21458 | . . 3 ⊢ ℤring = (ℂfld ↾s ℤ) | |
| 3 | cnfldbas 21368 | . . 3 ⊢ ℂ = (Base‘ℂfld) | |
| 4 | 2, 3 | ressbas2 17283 | . 2 ⊢ (ℤ ⊆ ℂ → ℤ = (Base‘ℤring)) |
| 5 | 1, 4 | ax-mp 5 | 1 ⊢ ℤ = (Base‘ℤring) |
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