Metamath Proof Explorer

Theorem qex

Description: The set of rational numbers exists. See also qexALT . (Contributed by NM, 30-Jul-2004) (Revised by Mario Carneiro, 17-Nov-2014)

Ref Expression
Assertion qex 
|- QQ e. _V

Proof

Step Hyp Ref Expression
1 cnex 
 |-  CC e. _V
2 qsscn 
 |-  QQ C_ CC
3 1 2 ssexi 
 |-  QQ e. _V