If \(x\) is a proposition, then the implication \(x\Rightarrow x\) is a tautology (i.e. always valid).
\(\text{"Socrates is a philosopher"}\Rightarrow \text{"Socrates is a philosopher"}\) is valid.
\(\text{"Socrates is not a philosopher"}\Rightarrow \text{"Socrates is not a philosopher"}\) is valid.
\(a=2\Rightarrow a=2\) is valid.
\(a\neq 2\Rightarrow a\neq 2\) is valid.
Proofs: 1