Or (minimal logic) §

Introduction Rule §

\frac{A}{A \lor B}$$\frac{B}{A \lor B}

Elimination Rule §

$\frac{\begin{array}{ccc}& [A{]}_i& [B{]}_i\\ & ⋮& ⋮\\ A\vee B& C& C\end{array}}{C}i$