Theorem bj-flddrng 34598

Description: Fields are division rings. (Contributed by BJ, 6-Jan-2024.)

Assertion

Ref	Expression
bj-flddrng	⊢ Field ⊆ DivRing

Proof of Theorem bj-flddrng

Step	Hyp	Ref	Expression
1		df-field 19498	. 2 ⊢ Field = (DivRing ∩ CRing)
2		inss1 4198	. 2 ⊢ (DivRing ∩ CRing) ⊆ DivRing
3	1, 2	eqsstri 3994	1 ⊢ Field ⊆ DivRing

Syntax hints:   ∩ cin 3928   ⊆ wss 3929  CRingccrg 19291  DivRingcdr 19495  Fieldcfield 19496

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1969  ax-7 2014  ax-8 2115  ax-9 2123  ax-10 2144  ax-11 2160  ax-12 2176  ax-ext 2792

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1539  df-ex 1780  df-nf 1784  df-sb 2069  df-clab 2799  df-cleq 2813  df-clel 2892  df-nfc 2962  df-v 3493  df-in 3936  df-ss 3945  df-field 19498

This theorem is referenced by:  bj-rrdrg  34599