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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 36823 | . 2 ⊢ Field ⊆ DivRing | |
2 | 1 | sseli 3968 | 1 ⊢ (𝐹 ∈ Field → 𝐹 ∈ DivRing) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 2098 DivRingcdr 20626 Fieldcfield 20627 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-ext 2696 |
This theorem depends on definitions: df-bi 206 df-an 395 df-tru 1536 df-ex 1774 df-sb 2060 df-clab 2703 df-cleq 2717 df-clel 2802 df-v 3465 df-in 3947 df-ss 3957 df-field 20629 |
This theorem is referenced by: (None) |
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