Theorem unifndxnn

Description: The index of the slot for the uniform set in an extensible structure is a positive integer. Formerly part of proof for tuslem . (Contributed by AV, 28-Oct-2024)

	Ref	Expression
Assertion	unifndxnn	$$⊢\mathrm{UnifSet}\left(\mathrm{ndx}\right)\in \mathbb{N}$$

Proof

Step	Hyp	Ref	Expression
1		unifndx	$$⊢\mathrm{UnifSet}\left(\mathrm{ndx}\right)=13$$
2		1nn0	$$⊢1\in {\mathbb{N}}_0$$
3		3nn	$$⊢3\in \mathbb{N}$$
4	2 3	decnncl	$$⊢13\in \mathbb{N}$$
5	1 4	eqeltri	$$⊢\mathrm{UnifSet}\left(\mathrm{ndx}\right)\in \mathbb{N}$$