Theorem bj-fldssdrng 37648

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 20704	. 2 ⊢ Field = (DivRing ∩ CRing)
2		inss1 4165	. 2 ⊢ (DivRing ∩ CRing) ⊆ DivRing
3	1, 2	eqsstri 3961	1 ⊢ Field ⊆ DivRing

Syntax hints:   ∩ cin 3882   ⊆ wss 3883  CRingccrg 20206  DivRingcdr 20701  Fieldcfield 20702

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2711

This theorem depends on definitions:  df-bi 208  df-an 397  df-tru 1550  df-ex 1787  df-sb 2074  df-clab 2718  df-cleq 2731  df-clel 2814  df-v 3433  df-in 3890  df-ss 3900  df-field 20704

This theorem is referenced by:  bj-flddrng  37649  bj-rrdrg  37650