Definition df-ndx 12465

Description: Define the structure component index extractor. See Theorem ndxarg 12485 to understand its purpose. The restriction to ℕ ensures that ndx is a set. The restriction to some set is necessary since I is a proper class. In principle, we could have chosen ℂ or (if we revise all structure component definitions such as df-base 12468) another set such as the set of finite ordinals ω (df-iom 4591). (Contributed by NM, 4-Sep-2011.)

Assertion

Ref	Expression
df-ndx	⊢ ndx = ( I ↾ ℕ)

Detailed syntax breakdown of Definition df-ndx

Step	Hyp	Ref	Expression
1		cnx 12459	. 2 class ndx
2		cid 4289	. . 3 class I
3		cn 8919	. . 3 class ℕ
4	2, 3	cres 4629	. 2 class ( I ↾ ℕ)
5	1, 4	wceq 1353	1 wff ndx = ( I ↾ ℕ)

This definition is referenced by:  ndxarg  12485