Theorem eufid

Description: Utility theorem: index-independent form of df-euf . (Contributed by Thierry Arnoux, 22-Mar-2025)

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

Proof

Step	Hyp	Ref	Expression
1		df-euf	$$⊢\mathrm{EuclF}=\mathrm{Slot}21$$
2		2nn0	$$⊢2\in {\mathbb{N}}_0$$
3		1nn	$$⊢1\in \mathbb{N}$$
4	2 3	decnncl	$$⊢21\in \mathbb{N}$$
5	1 4	ndxid	$$⊢\mathrm{EuclF}=\mathrm{Slot}\mathrm{EuclF}\left(\mathrm{ndx}\right)$$