Metamath Proof Explorer

Theorem nnrecq

Description: The reciprocal of a positive integer is rational. (Contributed by NM, 17-Nov-2004)

Ref Expression
Assertion nnrecq 
|- ( A e. NN -> ( 1 / A ) e. QQ )

Proof

Step Hyp Ref Expression
1 1z 
 |-  1 e. ZZ
2 znq 
 |-  ( ( 1 e. ZZ /\ A e. NN ) -> ( 1 / A ) e. QQ )
3 1 2 mpan 
 |-  ( A e. NN -> ( 1 / A ) e. QQ )