No rule, no. In an extended series of utterances, we tend to progress from indefinite article to definite article to possessive adjective, but it is only an observation: A bought a new hat today. The hat is quite attractive.
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Mister MicawberPlease notice, however, that #3 is singular, so that 'jaws' refers to a specific pair. 'The' would not sit so well in the other sentences with plural referents.Mister Micawber ,