Impossible Proposition Strictly Implies Every Proposition

Theorem

Let $P$ be a proposition of modal logic.

Let $P$ be not possibly true.

Then:

$\forall Q: P \implies Q$

where $Q$ is an arbitrary proposition in the universe of discourse.

Proof

This theorem requires a proof. In particular: More background needed into Modal Logic You 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

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): implication: 2. (strict implication)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): implication: 2. (strict implication)