Theorem bj-fldssdrng 37306

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 20692	. 2 ⊢ Field = (DivRing ∩ CRing)
2		inss1 4212	. 2 ⊢ (DivRing ∩ CRing) ⊆ DivRing
3	1, 2	eqsstri 4005	1 ⊢ Field ⊆ DivRing

Syntax hints:   ∩ cin 3925   ⊆ wss 3926  CRingccrg 20194  DivRingcdr 20689  Fieldcfield 20690

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2707

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2714  df-cleq 2727  df-clel 2809  df-v 3461  df-in 3933  df-ss 3943  df-field 20692

This theorem is referenced by:  bj-flddrng  37307  bj-rrdrg  37308