Necessary Proposition is Strictly Implied by Every Proposition
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Theorem
Let $P$ be a proposition of modal logic.
Let $P$ be necessarily true.
Then:
- $\forall Q: Q \implies P$
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)