Metamath Proof Explorer

Theorem nnrp

Description: A positive integer is a positive real. (Contributed by NM, 28-Nov-2008)

Ref Expression
Assertion nnrp 
|- ( A e. NN -> A e. RR+ )

Proof

Step Hyp Ref Expression
1 nnre 
 |-  ( A e. NN -> A e. RR )
2 nngt0 
 |-  ( A e. NN -> 0 < A )
3 elrp 
 |-  ( A e. RR+ <-> ( A e. RR /\ 0 < A ) )
4 1 2 3 sylanbrc 
 |-  ( A e. NN -> A e. RR+ )