Metamath Proof Explorer

Theorem homid

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

Ref Expression
Assertion homid 
|- Hom = Slot ( Hom ` ndx )

Proof

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