Prove using the definition of truth that for any first-order formula φ, φ is valid iff ∀x(φ) is valid.
It is given that is a first order formula.
Since is a formula it is a finite sequence of symbols from a given alphabet that is part of a formal language say .
A formula in a language is valid if it is true for every interpretation of .
In other words a formula is valid if and only if it is true for every .
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