Theorem bj-fldssdrng 38352

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 20998	. 2 ⊢ Field = (DivRing ∩ CRing)
2		inss1 4136	. 2 ⊢ (DivRing ∩ CRing) ⊆ DivRing
3	1, 2	eqsstri 3959	1 ⊢ Field ⊆ DivRing

This proof depends on syntax axioms:   ⊆ wss 3900   ∩ cin 4092  CRingccrg 20475  DivRingcdr 20995  Fieldcfield 20996

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1944  ax-6 2001  ax-7 2042  ax-8 2148  ax-9 2156  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1572  df-ex 1812  df-sb 2101  df-clab 2742  df-cleq 2755  df-clel 2839  df-v 3456  df-ss 3901  df-in 4094  df-field 20998

This theorem is used by:  bj-flddrng  38353  bj-rrdrg  38354