Theorem ltrelnq

Description: Positive fraction 'less than' is a relation on positive fractions. (Contributed by NM, 14-Feb-1996) (Revised by Mario Carneiro, 27-Apr-2013) (New usage is discouraged.)

	Ref	Expression
Assertion	ltrelnq	⊢ <Q ⊆ ( Q × Q )

Proof

Step	Hyp	Ref	Expression
1		df-ltnq	⊢ <Q = ( <pQ ∩ ( Q × Q ) )
2		inss2	⊢ ( <pQ ∩ ( Q × Q ) ) ⊆ ( Q × Q )
3	1 2	eqsstri	⊢ <Q ⊆ ( Q × Q )