Theorem edgfndxid

Description: The value of the edge function extractor is the value of the corresponding slot of the structure. (Contributed by AV, 21-Sep-2020)

	Ref	Expression
Assertion	edgfndxid	$$⊢G\in V\to \mathrm{ef}\left(G\right)=G\left(\mathrm{ef}\left(\mathrm{ndx}\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		id	$$⊢G\in V\to G\in V$$
2		df-edgf	$$⊢\mathrm{ef}=\mathrm{Slot}18$$
3		1nn0	$$⊢1\in {\mathbb{N}}_0$$
4		8nn	$$⊢8\in \mathbb{N}$$
5	3 4	decnncl	$$⊢18\in \mathbb{N}$$
6	1 2 5	strndxid	$$⊢G\in V\to G\left(\mathrm{ef}\left(\mathrm{ndx}\right)\right)=\mathrm{ef}\left(G\right)$$
7	6	eqcomd	$$⊢G\in V\to \mathrm{ef}\left(G\right)=G\left(\mathrm{ef}\left(\mathrm{ndx}\right)\right)$$