Does "if p=q, then nec(p=q)" hold, if "p" and "q" are intended to denote

Does "if p=q, then nec(p=q)" hold, if "p" and "q" are intended to denote

Does "if p=q, then nec(p=q)" hold, if "p" and "q" are intended to denote properties? I am told that it holds. But it doesn't seem to be quite right. It seems to depend on what it is for two properties to be identical. Am I confused?

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