{
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  "body": "\n## Summary\n\nIn predicate logic, **existential instantiation** (also called **existential elimination**) is a rule of inference which says that, given a formula of the form $(\\exists x) \\phi(x)$, one may infer $\\phi(c)$ for a new constant symbol *c*. The rule has the restrictions that the constant *c* introduced by the rule must be a new term that has not occurred earlier in the proof, and it also must not occur in the conclusion of the proof. It is also necessary that every instance of $x$ which is bound to $\\exists x$ must be uniformly replaced by *c*. This is implied by the notation $P\\left({a}\\right)$, but its explicit statement is often left out of explanations.\n",
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