Theorem bj-fldssdrng 35447

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 19984	. 2 ⊢ Field = (DivRing ∩ CRing)
2		inss1 4168	. 2 ⊢ (DivRing ∩ CRing) ⊆ DivRing
3	1, 2	eqsstri 3960	1 ⊢ Field ⊆ DivRing

Syntax hints:   ∩ cin 3891   ⊆ wss 3892  CRingccrg 19774  DivRingcdr 19981  Fieldcfield 19982

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 1975  ax-7 2015  ax-8 2112  ax-9 2120  ax-ext 2711

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1545  df-ex 1787  df-sb 2072  df-clab 2718  df-cleq 2732  df-clel 2818  df-v 3433  df-in 3899  df-ss 3909  df-field 19984

This theorem is referenced by:  bj-flddrng  35448  bj-rrdrg  35449