Theorem bj-fldssdrng 37854

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 20816	. 2 ⊢ Field = (DivRing ∩ CRing)
2		inss1 4197	. 2 ⊢ (DivRing ∩ CRing) ⊆ DivRing
3	1, 2	eqsstri 3991	1 ⊢ Field ⊆ DivRing

Syntax hints:   ∩ cin 3912   ⊆ wss 3913  CRingccrg 20316  DivRingcdr 20813  Fieldcfield 20814

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151  ax-9 2159  ax-ext 2741

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1570  df-ex 1807  df-sb 2098  df-clab 2748  df-cleq 2761  df-clel 2844  df-v 3465  df-in 3920  df-ss 3930  df-field 20816

This theorem is referenced by:  bj-flddrng  37855  bj-rrdrg  37856