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Template:MathJaxZach

Teorema$$\PageIndex{1}$$

Si$$c$$ es una constante que no ocurre en$$\Gamma$$ o$$A(x)$$ y$$\Gamma \Proves A(c)$$, entonces$$\Gamma \Proves \lforall{x}{A(x)}$$.

Prueba. Dejar$$\delta$$ ser una derivación$$A(c)$$ de$$\Gamma$$. Al agregar una$$\Intro{\lforall{}{}}$$ inferencia, obtenemos una prueba de$$\lforall{x}{A(x)}$$. Ya que$$c$$ no ocurre en$$\Gamma$$ o$$A(x)$$, se cumple la condición de variable propia. ◻

Proposición$$\PageIndex{1}$$

1. $$A(t) \Proves \lexists{x}{A(x)}$$.

2. $$\lforall{x}{A(x)} \Proves A(t)$$.

Prueba.

1. La siguiente es una derivación$$\lexists{x}{A(x)}$$ de$$A(t)$$:

2. La siguiente es una derivación$$A(t)$$ de$$\lforall{x}{A(x)}$$:

This page titled 9.10: Derivabilidad y los cuantificadores is shared under a CC BY license and was authored, remixed, and/or curated by Richard Zach et al. (Open Logic Project) .