Let x be continuous on x . Prove that is uniformly continuous on x .

I understand the concept of uniform continuity. I'm assuming it can't be all that more complicated for a rectangle.

My idea is that if we can show that is uniformly continuous on [a,b] and is uniformly continuous on [c,d] then f is uniformly continuous on [a,b]x[c,d]???

Any help would be appreciated.