I just meant that the guts of the proof of the EVT is BW added to the definition of continuity. That's all. Not that they are somehow formally equivalent. And yes, your proof was on the right track. I was thinking EVT was the continuous function bounded theorem. Just confused.
Oh, dear. I misunderstood you XD.
Yeah I already said that. I thought I was missing some cool relationship between both theorems.
Thanks for clarifying.