Definition df-lnr 37680

Description: A ring is left-Noetherian iff it is Noetherian as a left module over itself. (Contributed by Stefan O'Rear, 24-Jan-2015.)

Assertion

Ref	Expression
df-lnr	|- LNoeR = { a e. Ring | (ringLMod ` a ) e. LNoeM }

Detailed syntax breakdown of Definition df-lnr

Step	Hyp	Ref	Expression
1		clnr 37679	. 2 class LNoeR
2		va	. . . . . 6 setvar a
3	2	cv 1482	. . . . 5 class a
4		crglmod 19169	. . . . 5 class ringLMod
5	3, 4	cfv 5888	. . . 4 class (ringLMod ` a )
6		clnm 37645	. . . 4 class LNoeM
7	5, 6	wcel 1990	. . 3 wff (ringLMod ` a ) e. LNoeM
8		crg 18547	. . 3 class Ring
9	7, 2, 8	crab 2916	. 2 class { a e. Ring | (ringLMod ` a ) e. LNoeM }
10	1, 9	wceq 1483	1 wff LNoeR = { a e. Ring | (ringLMod ` a ) e. LNoeM }

This definition is referenced by:  islnr  37681