Theorem bj-fldssdrng 36659

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 20580	. 2 ⊢ Field = (DivRing ∩ CRing)
2		inss1 4220	. 2 ⊢ (DivRing ∩ CRing) ⊆ DivRing
3	1, 2	eqsstri 4008	1 ⊢ Field ⊆ DivRing

Syntax hints:   ∩ cin 3939   ⊆ wss 3940  CRingccrg 20129  DivRingcdr 20577  Fieldcfield 20578

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 2695

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-v 3468  df-in 3947  df-ss 3957  df-field 20580

This theorem is referenced by:  bj-flddrng  36660  bj-rrdrg  36661