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Suppose $\theta$ is a tautology and $A,B$ are sentence symbols occurring in $\theta$ and $\psi$ is a well formed formula obtained by replacing $B$ with $A.$ Is $\psi$ is a tautology?

My proof: We only need to consider any truth assignment $v$ such that $v(A)=v(B). $ Then $\bar v(\theta)=T$ and hence $\bar v(\psi)=T.$

Could anyone advise on my proof? Thank you.

Alexy Vincenzo
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  • $\theta$ ia a tautology becuase, for every truth assignment $v$ ... So why you consider $v(A)=v(B)$ ? You have that $v(\theta)=T$ both when $v(A)=T$ and $v(A)=F$, and these are the only possible cases. So, when you put $B$ in place of $A$ ... nothing changes. – Mauro ALLEGRANZA Feb 06 '14 at 14:13
  • put $A$ in place of $B$* – Alexy Vincenzo Feb 06 '14 at 14:33

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