Theorem bj-fldssdrng 37543

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 20677	. 2 ⊢ Field = (DivRing ∩ CRing)
2		inss1 4191	. 2 ⊢ (DivRing ∩ CRing) ⊆ DivRing
3	1, 2	eqsstri 3982	1 ⊢ Field ⊆ DivRing

Syntax hints:   ∩ cin 3902   ⊆ wss 3903  CRingccrg 20181  DivRingcdr 20674  Fieldcfield 20675

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-v 3444  df-in 3910  df-ss 3920  df-field 20677

This theorem is referenced by:  bj-flddrng  37544  bj-rrdrg  37545