Theorem homid

Description: Utility theorem: index-independent form of df-hom . (Contributed by Mario Carneiro, 7-Jan-2017)

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

Proof

Step	Hyp	Ref	Expression
1		df-hom	$$⊢\mathrm{Hom}=\mathrm{Slot}14$$
2		1nn0	$$⊢1\in {\mathbb{N}}_0$$
3		4nn	$$⊢4\in \mathbb{N}$$
4	2 3	decnncl	$$⊢14\in \mathbb{N}$$
5	1 4	ndxid	$$⊢\mathrm{Hom}=\mathrm{Slot}\mathrm{Hom}\left(\mathrm{ndx}\right)$$