Theorem flddivrng

Description: A field is a division ring. (Contributed by Jeff Madsen, 10-Jun-2010) (Revised by Mario Carneiro, 15-Dec-2013) (New usage is discouraged.)

	Ref	Expression
Assertion	flddivrng	|- ( K e. Fld -> K e. DivRingOps )

Proof

Step	Hyp	Ref	Expression
1		df-fld	|- Fld = ( DivRingOps i^i Com2 )
2		inss1	|- ( DivRingOps i^i Com2 ) C_ DivRingOps
3	1 2	eqsstri	|- Fld C_ DivRingOps
4	3	sseli	|- ( K e. Fld -> K e. DivRingOps )