Theorem dsndxnn

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

	Ref	Expression
Assertion	dsndxnn	⊢ ( dist ‘ ndx ) ∈ ℕ

Proof

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