Metamath Proof Explorer

Theorem ocid

Description: Utility theorem: index-independent form of df-ocomp . (Contributed by Mario Carneiro, 25-Oct-2015)

Ref Expression
Assertion ocid 
|- oc = Slot ( oc ` ndx )

Proof

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