Theorem bj-fldssdrng 37254

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 20754	. 2 ⊢ Field = (DivRing ∩ CRing)
2		inss1 4258	. 2 ⊢ (DivRing ∩ CRing) ⊆ DivRing
3	1, 2	eqsstri 4043	1 ⊢ Field ⊆ DivRing

Syntax hints:   ∩ cin 3975   ⊆ wss 3976  CRingccrg 20261  DivRingcdr 20751  Fieldcfield 20752

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-v 3490  df-in 3983  df-ss 3993  df-field 20754

This theorem is referenced by:  bj-flddrng  37255  bj-rrdrg  37256