Theorem bj-fldssdrng 37270

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 20748	. 2 ⊢ Field = (DivRing ∩ CRing)
2		inss1 4244	. 2 ⊢ (DivRing ∩ CRing) ⊆ DivRing
3	1, 2	eqsstri 4029	1 ⊢ Field ⊆ DivRing

Syntax hints:   ∩ cin 3961   ⊆ wss 3962  CRingccrg 20251  DivRingcdr 20745  Fieldcfield 20746

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004  ax-8 2107  ax-9 2115  ax-ext 2705

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1539  df-ex 1776  df-sb 2062  df-clab 2712  df-cleq 2726  df-clel 2813  df-v 3479  df-in 3969  df-ss 3979  df-field 20748

This theorem is referenced by:  bj-flddrng  37271  bj-rrdrg  37272