Metamath Proof Explorer


Theorem dsndx

Description: Index value of the df-ds slot. (Contributed by Mario Carneiro, 14-Aug-2015)

Ref Expression
Assertion dsndx ( dist ‘ ndx ) = 1 2

Proof

Step Hyp Ref Expression
1 df-ds dist = Slot 1 2
2 1nn0 1 ∈ ℕ0
3 2nn 2 ∈ ℕ
4 2 3 decnncl 1 2 ∈ ℕ
5 1 4 ndxarg ( dist ‘ ndx ) = 1 2