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	⊢ ( UnifSet ‘ ndx ) ∈ ℕ

Proof

Step	Hyp	Ref	Expression
1		unifndx	⊢ ( UnifSet ‘ ndx ) = ; 1 3
2		1nn0	⊢ 1 ∈ ℕ0
3		3nn	⊢ 3 ∈ ℕ
4	2 3	decnncl	⊢ ; 1 3 ∈ ℕ
5	1 4	eqeltri	⊢ ( UnifSet ‘ ndx ) ∈ ℕ