Theorem xrhaus

Description: The topology of the extended reals is Hausdorff. (Contributed by Thierry Arnoux, 24-Mar-2017)

	Ref	Expression
Assertion	xrhaus	$$⊢\mathrm{ordTop}\left(\le \right)\in \mathrm{Haus}$$

Proof

Step	Hyp	Ref	Expression
1		letsr	$$⊢\le \in \mathrm{TosetRel}$$
2		ordthaus	$$⊢\le \in \mathrm{TosetRel}\to \mathrm{ordTop}\left(\le \right)\in \mathrm{Haus}$$
3	1 2	ax-mp	$$⊢\mathrm{ordTop}\left(\le \right)\in \mathrm{Haus}$$