Theorem xrhaus

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

	Ref	Expression
Assertion	xrhaus	⊢ ( ordTop ‘ ≤ ) ∈ Haus

Proof

Step	Hyp	Ref	Expression
1		letsr	⊢ ≤ ∈ TosetRel
2		ordthaus	⊢ ( ≤ ∈ TosetRel → ( ordTop ‘ ≤ ) ∈ Haus )
3	1 2	ax-mp	⊢ ( ordTop ‘ ≤ ) ∈ Haus