Changes

<math>\{a \in x \mid \forall \text{x} \; A(\text{x}) \rightarrow {B}(\text{x}) \vdash A( a)\rightarrow B(a) \}</math>. <math>(1)</math>

<math>\{a \in x \mid \forall \text{x} \; A(\text{x}) \rightarrow {B}(\text{x}) \vdash A( a)\rightarrow B(a) \}</math>. <math>(1)</math>

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.

Llegados a este punto, también hay que considerar que la lógica de predicados no se utiliza sólo para demostrar que un determinado conjunto de premisas implica una determinada evidencia <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>demonstration by absurdity</u>. If its denial creates a contradiction, surely the dentist's proposition will be true: