Proof of commutativity for topological I-semigroups

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A topological semigroup on a closed interval I and order topology is called I-semigroup if 1 acts as an identity and 0 as an annihilator.

I've seen in several articles that such I-semigroups should be commutative. Where can I find a straightforward proof? (or, even better, can you suggest me a simple proof?)

Thank you!