Theorem bj-fldssdrng 37952

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 20830	. 2 ⊢ Field = (DivRing ∩ CRing)
2		inss1 4189	. 2 ⊢ (DivRing ∩ CRing) ⊆ DivRing
3	1, 2	eqsstri 3983	1 ⊢ Field ⊆ DivRing

Syntax hints:   ∩ cin 3904   ⊆ wss 3905  CRingccrg 20311  DivRingcdr 20827  Fieldcfield 20828

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1573  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-v 3457  df-in 3912  df-ss 3922  df-field 20830

This theorem is referenced by:  bj-flddrng  37953  bj-rrdrg  37954