Existential Generalisation/Proof System

Theorem

Let $\map {\mathbf A} x$ be a WFF of predicate Logic of $\LL$.

Let $\tau$ be a term which is freely substitutable for $x$ in $\mathbf A$.

Let $\mathscr H$ be Hilbert proof system instance 1 for predicate logic.


Then:

$\map {\mathbf A} \tau \vdash_{\mathscr H} \exists x: \map {\mathbf A} x$

is a provable consequence in $\mathscr H$.


Proof


Work In Progress
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by completing it.
To discuss this page in more detail, feel free to use the talk page.
When this work has been completed, you may remove this instance of {{WIP}} from the code.


Sources

  • 2009: Kenneth Kunen: The Foundations of Mathematics ... (previous) ... (next): $\text{II}.11$ Some Strategies for Constructing Proofs: Lemma $\text{II}.11.8$: Quantifier Rules (result statement)
This article is issued from ProofWiki. The text is available under Creative Commons Attribution-ShareAlike License unless otherwise noted. Additional terms may apply for the media files.