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Slim Jimmy is sure he'll bounce right back from his horrifying leg injury -- and while his confidence might be sizzurp-fueled ... he also thought he might die on stage when it first happened.

Slim and Swae Lee were on TMZ Live on Tuesday, and Slim described the moment he toppled into a spotlight, slashed his leg and toppled over during a show in NYC last weekend.

The guys were their usual light-hearted selves, but Slim got serious about the pain -- and then Swae quickly cracked a joke ... about his partner sipping on sizzurp (codeine cough syrup) during his hospital visit.

Check out the clip -- Slim thinks he'll be game ready within about 10 days. Mentally, he's already good-to-go ... these guys are awesome.