# Semantically Equivalent Terms are Equal

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## Theorem

Let $\tau_1, \tau_2$ be terms.

Suppose that they are semantically equivalent with respect to the empty set.

Then $\tau_1 = \tau_2$.

## Proof

This theorem requires a proof.In particular: While an exercise, this basically requires construction of the syntactic model in order to achieve full rigourYou can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.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 `{{ProofWanted}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |

## Sources

- 2009: Kenneth Kunen:
*The Foundations of Mathematics*... (previous) ... (next): $\mathrm{II}.8$ Further Semantic Notions: Exercise $\mathrm{II.8.5}$