Metamath Proof Explorer

Theorem nnrecred

Description: The reciprocal of a positive integer is real. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypothesis nnge1d.1 
|- ( ph -> A e. NN )
Assertion nnrecred 
|- ( ph -> ( 1 / A ) e. RR )

Proof

Step Hyp Ref Expression
1 nnge1d.1 
 |-  ( ph -> A e. NN )
2 nnrecre 
 |-  ( A e. NN -> ( 1 / A ) e. RR )
3 1 2 syl 
 |-  ( ph -> ( 1 / A ) e. RR )