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If a formula [tex]A[/tex] is provable without use of substitution axioms, nonlogical axioms, equality and identity axioms, and the [tex]\exists[/tex]-introduction rule, than [tex]A[/tex] is a tautology.

I try to act this way: consider a tautology A and show that using propositional axioms I get another tautology, and that if the hypothesis of a rule are tautologies then also the conclusion is a tautology. But I don't know wether it is the correct way or not.

Anyone can help me?

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# A formula provable without is a tautology

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