# Usuario:JULIAN.D.OR/ejercicio12

Ir a la navegación Ir a la búsqueda

Derivar ${\displaystyle \exists _{x}}$ ${\displaystyle \land }$ ${\displaystyle \forall _{x}}$${\displaystyle \forall _{y}}$( P( x ) ${\displaystyle \land }$ P( y ) ${\displaystyle \Rightarrow }$ ( x = y ) ) a partir de la premisa consistente en que ${\displaystyle \exists _{x}}$( P( x ) ${\displaystyle \land }$ ${\displaystyle \forall _{y}}$( P( y ) ${\displaystyle \Rightarrow }$ ( x = y ) ) )

1.${\displaystyle \exists _{x}}$( P( x ) ${\displaystyle \land }$ ${\displaystyle \forall _{y}}$( P( y ) ${\displaystyle \Rightarrow }$ ( x = y ) ) ) premisa

2.P( a ) ${\displaystyle \land }$ ${\displaystyle \forall _{y}}$( P( y ) ${\displaystyle \Rightarrow }$ ( a = y ) ) ${\displaystyle S_{a}^{x}}$ Particularizacion del Existencial 1.

3.${\displaystyle \forall _{y}}$( P( y ) ${\displaystyle \Rightarrow }$ ( a = y ) ) simplificacion 2.

4.P( y ) ${\displaystyle \Rightarrow }$ ( a = y ) ${\displaystyle S_{y}^{y}}$ Particularizcion del Universal 3.

5.P( a ) simplificacion 2.

6.P( a ) ${\displaystyle \land }$ P( y ) ${\displaystyle \Rightarrow }$ ( a = y ) combinacion 4. y 5.

7.${\displaystyle \forall _{y}}$( P( a ) ${\displaystyle \land }$ P( y ) ${\displaystyle \Rightarrow }$ ( a = y ) ) Generalizacion del Universal 6.

8.${\displaystyle \forall _{x}}$${\displaystyle \forall _{y}}$ ( P( x ) ${\displaystyle \land }$ P( y ) ${\displaystyle \Rightarrow }$ ( x = y ) ) Generalizacion del Universal 7.

9.${\displaystyle \exists _{x}}$P( x ) Generalizacion del Existencial

10.${\displaystyle \exists _{x}}$P( x ) ${\displaystyle \land }$ ${\displaystyle \forall _{x}}$${\displaystyle \forall _{y}}$ ( P( x ) ${\displaystyle \land }$ P( y ) ${\displaystyle \Rightarrow }$ ( x = y ) ) combinacion 8. y 9.