Metamath Proof Explorer


Theorem nqex

Description: The class of positive fractions exists. (Contributed by NM, 16-Aug-1995) (Revised by Mario Carneiro, 27-Apr-2013) (New usage is discouraged.)

Ref Expression
Assertion nqex Q ∈ V

Proof

Step Hyp Ref Expression
1 df-nq Q = { 𝑦 ∈ ( N × N ) ∣ ∀ 𝑥 ∈ ( N × N ) ( 𝑦 ~Q 𝑥 → ¬ ( 2nd𝑥 ) <N ( 2nd𝑦 ) ) }
2 niex N ∈ V
3 2 2 xpex ( N × N ) ∈ V
4 1 3 rabex2 Q ∈ V