Metamath Proof Explorer

Theorem ccoid

Description: Utility theorem: index-independent form of df-cco . (Contributed by Mario Carneiro, 7-Jan-2017)

Ref Expression
Assertion ccoid 
|- comp = Slot ( comp ` ndx )

Proof

Step Hyp Ref Expression
1 df-cco 
 |-  comp = Slot ; 1 5
2 1nn0 
 |-  1 e. NN0
3 5nn 
 |-  5 e. NN
4 2 3 decnncl 
 |-  ; 1 5 e. NN
5 1 4 ndxid 
 |-  comp = Slot ( comp ` ndx )