Theorem bj-fldssdrng 37991

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

Assertion

Ref	Expression
bj-fldssdrng	⊢ Field ⊆ DivRing

Proof of Theorem bj-fldssdrng

Step	Hyp	Ref	Expression
1		df-field 20882	. 2 ⊢ Field = (DivRing ∩ CRing)
2		inss1 4189	. 2 ⊢ (DivRing ∩ CRing) ⊆ DivRing
3	1, 2	eqsstri 3984	1 ⊢ Field ⊆ DivRing

This proof depends on syntax axioms:   ∩ cin 3905   ⊆ wss 3906  CRingccrg 20362  DivRingcdr 20879  Fieldcfield 20880

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2148  ax-9 2156  ax-ext 2737

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2744  df-cleq 2757  df-clel 2840  df-v 3459  df-in 3913  df-ss 3923  df-field 20882

This theorem is used by:  bj-flddrng  37992  bj-rrdrg  37993