A [[Proof|proof]] (or deductive) system $F$ consists a set of derivation rules: rules for logical operators.
A system is sound and complete iff for any set of $L_{2}$ sentences $\varphi_1,...\varphi_{n},$ and $L_2$ sentence $\psi$, $\varphi_1,...\varphi_{n} \vdash \psi$ iff the argument in which $\varphi_1,\ldots\varphi_n$ are the premises and $\psi$ is the conclusion is [[Logically Valid Argument|logically valid]].
## Examples
- [[Fitch System for L2]].
- [[Fitch System for L1p]].