Metamath Proof Explorer

Theorem nn0absid

Description: A nonnegative integer is its own absolute value. (Contributed by AV, 22-Nov-2025)

Ref Expression
Assertion nn0absid 
|- ( N e. NN0 -> ( abs ` N ) = N )

Proof

Step Hyp Ref Expression
1 nn0re 
 |-  ( N e. NN0 -> N e. RR )
2 nn0ge0 
 |-  ( N e. NN0 -> 0 <_ N )
3 1 2 absidd 
 |-  ( N e. NN0 -> ( abs ` N ) = N )