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| Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-flddrng | Structured version Visualization version GIF version | ||
| Description: Fields are division rings (elemental version). (Contributed by BJ, 9-Nov-2024.) |
| Ref | Expression |
|---|---|
| bj-flddrng | ⊢ (𝐹 ∈ Field → 𝐹 ∈ DivRing) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | bj-fldssdrng 37289 | . 2 ⊢ Field ⊆ DivRing | |
| 2 | 1 | sseli 3979 | 1 ⊢ (𝐹 ∈ Field → 𝐹 ∈ DivRing) |
| Colors of variables: wff setvar class |
| Syntax hints: → wi 4 ∈ wcel 2108 DivRingcdr 20729 Fieldcfield 20730 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1543 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-v 3482 df-in 3958 df-ss 3968 df-field 20732 |
| This theorem is referenced by: (None) |
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