Theorem lngid

Description: Utility theorem: index-independent form of df-lng . (Contributed by Thierry Arnoux, 27-Mar-2019)

	Ref	Expression
Assertion	lngid	$$⊢{Line}_{𝒢}=\mathrm{Slot}{Line}_{𝒢}\left(\mathrm{ndx}\right)$$

Proof

Step	Hyp	Ref	Expression
1		df-lng	$$⊢{Line}_{𝒢}=\mathrm{Slot}17$$
2		1nn0	$$⊢1\in {\mathbb{N}}_0$$
3		7nn	$$⊢7\in \mathbb{N}$$
4	2 3	decnncl	$$⊢17\in \mathbb{N}$$
5	1 4	ndxid	$$⊢{Line}_{𝒢}=\mathrm{Slot}{Line}_{𝒢}\left(\mathrm{ndx}\right)$$