Theorem dsid

Description: Utility theorem: index-independent form of df-ds . (Contributed by Mario Carneiro, 23-Dec-2013)

	Ref	Expression
Assertion	dsid	$$⊢\mathrm{dist}=\mathrm{Slot}\mathrm{dist}\left(\mathrm{ndx}\right)$$

Proof

Step	Hyp	Ref	Expression
1		df-ds	$$⊢\mathrm{dist}=\mathrm{Slot}12$$
2		1nn0	$$⊢1\in {\mathbb{N}}_0$$
3		2nn	$$⊢2\in \mathbb{N}$$
4	2 3	decnncl	$$⊢12\in \mathbb{N}$$
5	1 4	ndxid	$$⊢\mathrm{dist}=\mathrm{Slot}\mathrm{dist}\left(\mathrm{ndx}\right)$$