Metamath Proof Explorer

Theorem nn0negz

Description: The negative of a nonnegative integer is an integer. (Contributed by NM, 9-May-2004)

Ref Expression
Assertion nn0negz 
|- ( N e. NN0 -> -u N e. ZZ )

Proof

Step Hyp Ref Expression
1 nn0z 
 |-  ( N e. NN0 -> N e. ZZ )
2 znegcl 
 |-  ( N e. ZZ -> -u N e. ZZ )
3 1 2 syl 
 |-  ( N e. NN0 -> -u N e. ZZ )