Metamath Proof Explorer


Theorem uzval

Description: The value of the upper integers function. (Contributed by NM, 5-Sep-2005) (Revised by Mario Carneiro, 3-Nov-2013)

Ref Expression
Assertion uzval N N = k | N k

Proof

Step Hyp Ref Expression
1 breq1 j = N j k N k
2 1 rabbidv j = N k | j k = k | N k
3 df-uz = j k | j k
4 zex V
5 4 rabex k | N k V
6 2 3 5 fvmpt N N = k | N k