Theorem bj-fldssdrng 35438

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 19975	. 2 ⊢ Field = (DivRing ∩ CRing)
2		inss1 4167	. 2 ⊢ (DivRing ∩ CRing) ⊆ DivRing
3	1, 2	eqsstri 3959	1 ⊢ Field ⊆ DivRing

Syntax hints:   ∩ cin 3890   ⊆ wss 3891  CRingccrg 19765  DivRingcdr 19972  Fieldcfield 19973

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1801  ax-4 1815  ax-5 1916  ax-6 1974  ax-7 2014  ax-8 2111  ax-9 2119  ax-ext 2710

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1544  df-ex 1786  df-sb 2071  df-clab 2717  df-cleq 2731  df-clel 2817  df-v 3432  df-in 3898  df-ss 3908  df-field 19975

This theorem is referenced by:  bj-flddrng  35439  bj-rrdrg  35440