Metamath Proof Explorer

Theorem qdencl

Description: The canonical denominator is a positive integer. (Contributed by Stefan O'Rear, 13-Sep-2014)

Ref Expression
Assertion qdencl 
|- ( A e. QQ -> ( denom ` A ) e. NN )

Proof

Step Hyp Ref Expression
1 qnumdencl 
 |-  ( A e. QQ -> ( ( numer ` A ) e. ZZ /\ ( denom ` A ) e. NN ) )
2 1 simprd 
 |-  ( A e. QQ -> ( denom ` A ) e. NN )