Metamath Proof Explorer


Theorem lngid

Description: Utility theorem: index-independent form of df-lng . (Contributed by Thierry Arnoux, 27-Mar-2019)

Ref Expression
Assertion lngid LineG = Slot ( LineG ‘ ndx )

Proof

Step Hyp Ref Expression
1 df-lng LineG = Slot 1 7
2 1nn0 1 ∈ ℕ0
3 7nn 7 ∈ ℕ
4 2 3 decnncl 1 7 ∈ ℕ
5 1 4 ndxid LineG = Slot ( LineG ‘ ndx )