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At this point, it must also be considered that predicate logic is not used only to prove that a particular set of premises imply a particular evidence <math>(1)</math>. It is also used to prove that a particular assertion is not true, or that a particular piece of knowledge is logically compatible/incompatible with a particular evidence.

At this point, it must also be considered that predicate logic is not used only to prove that a particular set of premises imply a particular evidence <math>(1)</math>. It is also used to prove that a particular assertion is not true, or that a particular piece of knowledge is logically compatible/incompatible with a particular evidence.

In order to prove that this proposition is true we must use the above mentioned<u>demonstration by absurdity</u>. If its denial creates a contradiction, surely the dentist's proposition will be true:

In order to prove that this proposition is true we must use the above mentioned<u>dimostrazione per assurdo</u>. If its denial creates a contradiction, surely the dentist's proposition will be true:

<math>\urcorner\{a \in x \mid \forall \text{x} \; A(\text{x}) \rightarrow {B}(\text{x}) \vdash A( a)\rightarrow B(a) \}</math>. <math>(2)</math>

<math>\urcorner\{a \in x \mid \forall \text{x} \; A(\text{x}) \rightarrow {B}(\text{x}) \vdash A( a)\rightarrow B(a) \}</math>. <math>(2)</math>