# Existential instantiation

In predicate logic, **existential instantiation** (also called **existential elimination**)[1][2][3] is a valid rule of inference which says that, given a formula of the form
, one may infer
for a new constant symbol *c*. The rule has the restriction that the constant *c* introduced by the rule must be a new term that has not occurred earlier in the proof.

Transformation rules |
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Propositional calculus |

Rules of inference |

Rules of replacement |

Predicate logic |

In one formal notation, the rule may be denoted by

where *a* is a new constant symbol that has not appeared in the proof.

## References

- Hurley, Patrick.
*A Concise Introduction to Logic*. Wadsworth Pub Co, 2008. - Copi and Cohen
- Moore and Parker

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