Imagine we have two names, X and Y, which describe the same object.
If X and Y are identical in every possible way, and therefore X=Y, is
X is like Y.
a true statement?
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If something is identical (X==Y) then it is necessarily alike (but more than that)
If something is alike, it is not necessarily identical.
X equals / is identical to Y is thus a stronger / stricter statement (than alike)
So, as Weather Vane said in his comment, "X and Y are alike" is not a false statement, but it is one you would not say, as you already said (or if you haven't, you should say [because it provides more information]) that "X and Y are identical".
Saying "X is like Y" after saying they are identical actually takes away from the strength of the identical statement (and is confusing because why would you partially/potentially negate what you just said).