Theorem bj-flddrng 34573

Description: Fields are division rings. (Contributed by BJ, 6-Jan-2024.)

Assertion

Ref	Expression
bj-flddrng	⊢ Field ⊆ DivRing

Proof of Theorem bj-flddrng

Step	Hyp	Ref	Expression
1		df-field 19505	. 2 ⊢ Field = (DivRing ∩ CRing)
2		inss1 4205	. 2 ⊢ (DivRing ∩ CRing) ⊆ DivRing
3	1, 2	eqsstri 4001	1 ⊢ Field ⊆ DivRing

Syntax hints:   ∩ cin 3935   ⊆ wss 3936  CRingccrg 19298  DivRingcdr 19502  Fieldcfield 19503

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2177  ax-ext 2793

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1540  df-ex 1781  df-nf 1785  df-sb 2070  df-clab 2800  df-cleq 2814  df-clel 2893  df-nfc 2963  df-v 3496  df-in 3943  df-ss 3952  df-field 19505

This theorem is referenced by:  bj-rrdrg  34574