Theorem qtopbas

Description: The set of open intervals with rational endpoints forms a basis for a topology. (Contributed by NM, 8-Mar-2007)

	Ref	Expression
Assertion	qtopbas	⊢ ( (,) “ ( ℚ × ℚ ) ) ∈ TopBases

Proof

Step	Hyp	Ref	Expression
1		qssre	⊢ ℚ ⊆ ℝ
2		ressxr	⊢ ℝ ⊆ ℝ*
3	1 2	sstri	⊢ ℚ ⊆ ℝ*
4	3	qtopbaslem	⊢ ( (,) “ ( ℚ × ℚ ) ) ∈ TopBases