Thread:DarkJaguar124/@comment-809585-20150311170758

Reading from it, it doesn't really elaborate much. It simply mentions that there's two, it doesn't flat out say it's Kuai OR Bi-Han.

"Sub-Zero

Kuai Liang and his older brother Bi-Han served the Lin Kuei assassin clan faithfully until the first Mortal Kombat tournament. There Bi-Han, code-named Sub-Zero, was killed by the demon Scorpion. Kuai Liang assumed the Sub-Zero mantle and went to Outworld to find his brother's killer."

Simply stating that, after Bi-Han's death Kuai assumed the mantle of Sub-Zero. 