Existential Generalisation/Informal Statement

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$\map P {\mathbf a} \vdash \exists x: \map P x$

Suppose we have the following:

We can find an arbitrary object $\mathbf a$ in our universe of discourse which has the property $P$.

Then we may infer that:

there exists in that universe at least one object $x$ which has that property $P$.

This is called the Rule of Existential Generalisation and often appears in a proof with its abbreviation $\text {EG}$.