Metamath Proof Explorer

Theorem zabscl

Description: The absolute value of an integer is an integer. (Contributed by Stefan O'Rear, 24-Sep-2014)

Ref Expression
Assertion zabscl 
|- ( A e. ZZ -> ( abs ` A ) e. ZZ )

Proof

Step Hyp Ref Expression
1 nn0abscl 
 |-  ( A e. ZZ -> ( abs ` A ) e. NN0 )
2 1 nn0zd 
 |-  ( A e. ZZ -> ( abs ` A ) e. ZZ )