Theorem bj-fldssdrng 37780

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 20782	. 2 ⊢ Field = (DivRing ∩ CRing)
2		inss1 4188	. 2 ⊢ (DivRing ∩ CRing) ⊆ DivRing
3	1, 2	eqsstri 3982	1 ⊢ Field ⊆ DivRing

Syntax hints:   ∩ cin 3903   ⊆ wss 3904  CRingccrg 20284  DivRingcdr 20779  Fieldcfield 20780

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1815  ax-4 1829  ax-5 1930  ax-6 1987  ax-7 2028  ax-8 2144  ax-9 2152  ax-ext 2734

This theorem depends on definitions:  df-bi 209  df-an 400  df-tru 1563  df-ex 1800  df-sb 2091  df-clab 2741  df-cleq 2754  df-clel 2837  df-v 3456  df-in 3911  df-ss 3921  df-field 20782

This theorem is referenced by:  bj-flddrng  37781  bj-rrdrg  37782