User:Ascii/Propositional Logic/Implication
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The following is a list of theorems in propositional logic with the only logical connective featured being implication.
Featuring $1$ Propositional Variable
| Page | Subpages and Formulations | Theorem |
|---|---|---|
| Law of Identity | Formulation 1 | $p \vdash p$ |
| Formulation 2 | $\vdash p \implies p$ | |
| Self-Distributive Law for Conditional | Forward Implication/Formulation 1 | $p \implies \left({q \implies r}\right) \vdash \left({p \implies q}\right) \implies \left({p \implies r}\right)$ |
| Reverse Implication/Formulation 1 | $\left({p \implies q}\right) \implies \left({p \implies r}\right) \vdash p \implies \left({q \implies r}\right)$ |