Theorem letopon

Description: The topology of the extended reals. (Contributed by Mario Carneiro, 3-Sep-2015)

	Ref	Expression
Assertion	letopon	⊢ ( ordTop ‘ ≤ ) ∈ ( TopOn ‘ ℝ* )

Proof

Step	Hyp	Ref	Expression
1		letsr	⊢ ≤ ∈ TosetRel
2		ledm	⊢ ℝ* = dom ≤
3	2	ordttopon	⊢ ( ≤ ∈ TosetRel → ( ordTop ‘ ≤ ) ∈ ( TopOn ‘ ℝ* ) )
4	1 3	ax-mp	⊢ ( ordTop ‘ ≤ ) ∈ ( TopOn ‘ ℝ* )