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Theorem bj-flddrng 37290
Description: Fields are division rings (elemental version). (Contributed by BJ, 9-Nov-2024.)
Assertion
Ref Expression
bj-flddrng (𝐹 ∈ Field → 𝐹 ∈ DivRing)

Proof of Theorem bj-flddrng
StepHypRef Expression
1 bj-fldssdrng 37289 . 2 Field ⊆ DivRing
21sseli 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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