Metamath Proof Explorer

Theorem nn0rp0

Description: A nonnegative integer is a nonnegative real number. (Contributed by AV, 24-May-2020)

Ref Expression
Assertion nn0rp0 
|- ( N e. NN0 -> N e. ( 0 [,) +oo ) )

Proof

Step Hyp Ref Expression
1 nn0re 
 |-  ( N e. NN0 -> N e. RR )
2 nn0ge0 
 |-  ( N e. NN0 -> 0 <_ N )
3 elrege0 
 |-  ( N e. ( 0 [,) +oo ) <-> ( N e. RR /\ 0 <_ N ) )
4 1 2 3 sylanbrc 
 |-  ( N e. NN0 -> N e. ( 0 [,) +oo ) )