Theorem bj-fldssdrng 37008

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 20706	. 2 ⊢ Field = (DivRing ∩ CRing)
2		inss1 4227	. 2 ⊢ (DivRing ∩ CRing) ⊆ DivRing
3	1, 2	eqsstri 4013	1 ⊢ Field ⊆ DivRing

Syntax hints:   ∩ cin 3945   ⊆ wss 3946  CRingccrg 20213  DivRingcdr 20703  Fieldcfield 20704

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2697

This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1537  df-ex 1775  df-sb 2061  df-clab 2704  df-cleq 2718  df-clel 2803  df-v 3464  df-in 3953  df-ss 3963  df-field 20706

This theorem is referenced by:  bj-flddrng  37009  bj-rrdrg  37010