Definition df-rgmod 17176

Description: Every ring can be viewed as a left module over itself. (Contributed by Stefan O'Rear, 6-Dec-2014.)

Assertion

Ref	Expression
df-rgmod	|- ringLMod = ( w e. _V |-> ( (subringAlg ` w ) ` ( Base ` w ) ) )

Detailed syntax breakdown of Definition df-rgmod

Step	Hyp	Ref	Expression
1		crglmod 17172	. 2 class ringLMod
2		vw	. . 3 setvar w
3		cvv 2962	. . 3 class _V
4	2	cv 1361	. . . . 5 class w
5		cbs 14157	. . . . 5 class Base
6	4, 5	cfv 5406	. . . 4 class ( Base ` w )
7		csra 17171	. . . . 5 class subringAlg
8	4, 7	cfv 5406	. . . 4 class (subringAlg ` w )
9	6, 8	cfv 5406	. . 3 class ( (subringAlg ` w ) ` ( Base ` w ) )
10	2, 3, 9	cmpt 4338	. 2 class ( w e. _V |-> ( (subringAlg ` w ) ` ( Base ` w ) ) )
11	1, 10	wceq 1362	1 wff ringLMod = ( w e. _V |-> ( (subringAlg ` w ) ` ( Base ` w ) ) )

This definition is referenced by:  rlmfn  17193  rlmval  17194