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Theorem bj-flddrng 35194
Description: Fields are division rings. (Contributed by BJ, 6-Jan-2024.)
Assertion
Ref Expression
bj-flddrng Field ⊆ DivRing

Proof of Theorem bj-flddrng
StepHypRef Expression
1 df-field 19770 . 2 Field = (DivRing ∩ CRing)
2 inss1 4143 . 2 (DivRing ∩ CRing) ⊆ DivRing
31, 2eqsstri 3935 1 Field ⊆ DivRing
Colors of variables: wff setvar class
Syntax hints:  cin 3865  wss 3866  CRingccrg 19563  DivRingcdr 19767  Fieldcfield 19768
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-8 2112  ax-9 2120  ax-ext 2708
This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1546  df-ex 1788  df-sb 2071  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3410  df-in 3873  df-ss 3883  df-field 19770
This theorem is referenced by:  bj-rrdrg  35195
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