As for me you can omit the but you shouldn't as you are talking about the defined ice(the ice which was on the stairs)...
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AnonymousI'm not sure whether "ice" in my sentece requires definite article. Can you tell me if I can omit it?No, you can't omit it. It's clear which ice it is. It's the ice that was on the stairs, not just any ice anywhere in the world.
"He slipped on the stairs because he didn't remove the ice".