In the Practical English Usage 3rd, it says:

Letters which begin Dear Sir(s) or Dear Madam usually finish Yours faithfully in British English. Formal letters which begin with the person's name (e.g. Dear Miss Haiokins, Dear Peter Lewis) usually finish Yours sincerely.

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What does 'Yours faithfully/sincerely' here mean?
Does it mean 'I am faithfully/sincerely your servant'?