Metamath Proof Explorer

Theorem nnrecre

Description: The reciprocal of a positive integer is real. (Contributed by NM, 8-Feb-2008)

Ref Expression
Assertion nnrecre 
|- ( N e. NN -> ( 1 / N ) e. RR )

Proof

Step Hyp Ref Expression
1 1re 
 |-  1 e. RR
2 nndivre 
 |-  ( ( 1 e. RR /\ N e. NN ) -> ( 1 / N ) e. RR )
3 1 2 mpan 
 |-  ( N e. NN -> ( 1 / N ) e. RR )