Metamath Proof Explorer


Theorem eufndx

Description: Index value of the Euclidean function slot. Use ndxarg . (Contributed by Thierry Arnoux, 22-Mar-2025) (New usage is discouraged.)

Ref Expression
Assertion eufndx ( EuclF ‘ ndx ) = 2 1

Proof

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