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 e. NN0
3 7nn 
 |-  7 e. NN
4 2 3 decnncl 
 |-  ; 1 7 e. NN
5 1 4 ndxid 
 |-  LineG = Slot ( LineG ` ndx )