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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 → ¬ ( 2^nd ‘ 𝑥 ) <_N ( 2^nd ‘ 𝑦 ) ) }
2		niex	⊢ N ∈ V
3	2 2	xpex	⊢ ( N × N ) ∈ V
4	1 3	rabex2	⊢ Q ∈ V