True Statement is implied by Every Statement/Formulation 2/Proof by Truth Table

Theorem

 * $\vdash q \implies \left({p \implies q}\right)$

Proof
We apply the Method of Truth Tables.

As can be seen by inspection, the truth value under the main connective, the first instance of $\implies$, is $T$ for each boolean interpretation.

$\begin{array}{|ccccc|} \hline q & \implies & ( p & \implies & q ) \\ \hline F & T & T & F & F \\ F & T & F & T & F \\ T & T & T & T & T \\ T & T & F & T & T \\ \hline \end{array}$