Theorem xlimrel

Description: The limit on extended reals is a relation. (Contributed by Glauco Siliprandi, 5-Feb-2022)

	Ref	Expression
Assertion	xlimrel	⊢ Rel ~~>*

Proof

Step	Hyp	Ref	Expression
1		lmrel	⊢ Rel ( ⇝𝑡 ‘ ( ordTop ‘ ≤ ) )
2		df-xlim	⊢ ~~>* = ( ⇝𝑡 ‘ ( ordTop ‘ ≤ ) )
3	2	releqi	⊢ ( Rel ~~>* ↔ Rel ( ⇝𝑡 ‘ ( ordTop ‘ ≤ ) ) )
4	1 3	mpbir	⊢ Rel ~~>*