...Huh? 0 what?
The normal boiling point of water is 100.00∘C, and the normal freezing point of water is indisputably 0.00∘C. There is no need to discuss the so-called "vaporization point" because it's a synonym... (for what?)
The phase diagram here quite clearly proves it.
https://s3-us-west-2.amazonaws.com/
The "normal" phase transition temperatures by definition are the temperatures at 1.00 atm where phase transitions will occur.
If you cross a phase coexistence curve (such as ¯¯¯¯¯¯AD or ¯¯¯¯¯¯AE), you transition to another phase. The easiest and most common way to do that is to heat or cool, i.e. move horizontally. Rightwards = heating up.
Hence, at 1.00 atm, the normal freezing/melting point is at 0.00∘C and the normal boiling/condensation point is at 100.00∘C, as indicated by the dotted lines and, well, the words on the image.
QED
So, can you "prove" that the critical point is at 373.99∘C and 217.75 atm? Can you convince yourself that the triple point is at 0.0060 atm and 0.01∘C?