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Metamath Proof Explorer

Theorem reopn

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

		Ref	Expression
	Assertion	reopn	$⊢ ℝ \in topGen (ran (.))$

Step	Hyp	Ref	Expression
1		retop	$⊢ topGen (ran (.)) \in Top$
2		uniretop	$⊢ ℝ = ⋃ topGen (ran (.))$
3	2	topopn	$⊢ topGen (ran (.)) \in Top \to ℝ \in topGen (ran (.))$
4	1 3	ax-mp	$⊢ ℝ \in topGen (ran (.))$