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Answer by Doug Spoonwood for Does the Definition of a Formal Proof in...
It forbids substitutions in theorems in formal proofs (NO formal proofs exist in the book... not a single one). But, that is not generally how the axiomatic method has gotten used historically speaking.
View ArticleAnswer by user21820 for Does the Definition of a Formal Proof in Mendelson's...
By the very definition you gave, clearly a proof can only use the given rules of inference and hence cannot invoke theorems in the meta-system. A common meta-theorem is the deduction theorem, namely...
View ArticleDoes the Definition of a Formal Proof in Mendelson's Book Allow for the Use...
The relevance of this question concerns deciding whether or not a sequence of well-formed formulas in a text will qualify as a formal proof.Mendelson's Introduction to Mathematical Logic on p. 25 of...
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