Theorem ocid

Description: Utility theorem: index-independent form of df-ocomp . (Contributed by Mario Carneiro, 25-Oct-2015)

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

Proof

Step	Hyp	Ref	Expression
1		df-ocomp	$$⊢\mathrm{oc}=\mathrm{Slot}11$$
2		1nn0	$$⊢1\in {\mathbb{N}}_0$$
3		1nn	$$⊢1\in \mathbb{N}$$
4	2 3	decnncl	$$⊢11\in \mathbb{N}$$
5	1 4	ndxid	$$⊢\mathrm{oc}=\mathrm{Slot}\mathrm{oc}\left(\mathrm{ndx}\right)$$