Theorem reopn

Description: The reals are open with respect to the standard topology. (Contributed by Glauco Siliprandi, 11-Dec-2019)

	Ref	Expression
Assertion	reopn	⊢ ℝ ∈ ( topGen ‘ ran (,) )

Proof

Step	Hyp	Ref	Expression
1		retop	⊢ ( topGen ‘ ran (,) ) ∈ Top
2		uniretop	⊢ ℝ = ∪ ( topGen ‘ ran (,) )
3	2	topopn	⊢ ( ( topGen ‘ ran (,) ) ∈ Top → ℝ ∈ ( topGen ‘ ran (,) ) )
4	1 3	ax-mp	⊢ ℝ ∈ ( topGen ‘ ran (,) )