Every first-order logic formula which has a tautological shape in propositional logic is a valid formula. Is it possible to give a formal proof for the above?
Proof of validity of tautology in first order logic
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logic
proof-writing
propositional-calculus
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0Yes it is indeed possible to give a formal proof. And it is proved in many textbooks. Which have you looked at? – 2012-11-06
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0i hav not looked at any textbooks as yet.can you please give any reference.so far i have been sticking to my notes only. – 2012-11-06
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0I know not the tastes of others, but I learned my set theory from [Bourbaki](http://books.google.com.tw/books?id=IL-SI67hjI4C&printsec=frontcover&dq=Bourbaki%2Bset+theory&hl=fr&sa=X&ei=GU-ZUOjCIc3tmAWjpoDYBw&sqi=2&redir_esc=y#v=onepage&q=Bourbaki%2Bset%20theory&f=false).Hope you like it. – 2012-11-06
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3You might want to take a look at Enderton, H. B. (2002) *A Mathematical Introduction to Logic*, Harcourt/Academic Press, ISBN 0-12-238452-0. Note that in first order logic, such tautologies (or formulas which have "tautological shape in propositional logic) are a proper subset of logically valid formulas, which I presume you know. – 2012-11-06