Definition df-lvec

Description: Define the class of all left vector spaces. A left vector space over a division ring is an Abelian group (vectors) together with a division ring (scalars) and a left scalar product connecting them. Some authors call this a "left module over a division ring", reserving "vector space" for those where the division ring is commutative, i.e., is a field. (Contributed by NM, 11-Nov-2013)

	Ref	Expression
Assertion	df-lvec	|- LVec = { f e. LMod | ( Scalar ` f ) e. DivRing }

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		clvec	|- LVec
1		vf	|- f
2		clmod	|- LMod
3		csca	|- Scalar
4	1	cv	|- f
5	4 3	cfv	|- ( Scalar ` f )
6		cdr	|- DivRing
7	5 6	wcel	|- ( Scalar ` f ) e. DivRing
8	7 1 2	crab	|- { f e. LMod | ( Scalar ` f ) e. DivRing }
9	0 8	wceq	|- LVec = { f e. LMod | ( Scalar ` f ) e. DivRing }