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 ) e. NN

Proof

Step	Hyp	Ref	Expression
1		dsndx	|- ( dist ` ndx ) = ; 1 2
2		1nn0	|- 1 e. NN0
3		2nn	|- 2 e. NN
4	2 3	decnncl	|- ; 1 2 e. NN
5	1 4	eqeltri	|- ( dist ` ndx ) e. NN