Does s/o want to check whether a proof I did is free of errors/omissions? Here's the proposition that should be proved: Every space that is both T1 and normal is also Hausdorff.
And here my tentative to prove this: Let {a} and {b} be two arbitrary singleton sets. In a T1-space these sets are closed. As the space is also normal there exist two disjoint open sets U,V with {a} a subset of U and {b} a subset of V. This also means that for arbitrary points a,b there exist disjoint open sets U,V with a in U and b in V which is precisely the Hausdorff condition.

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as i recall "normal" is the same as T4 right?

normal + T1 is the same as T4

so disjoint closed sets A, B are contained in disjoint open sets

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