True Statement is implied by Every Statement/Formulation 1/Proof by Truth Table

Theorem

 * $p \vdash q \implies p$

Proof
We apply the Method of Truth Tables.

As can be seen by inspection, where the truth value in the relevant column on the LHS is $T$, that under the one on the RHS is also $T$:

$\begin{array}{|c||ccc|} \hline p & q & \implies & p \\ \hline F & F & T & F \\ F & T & F & F \\ T & F & T & T \\ T & T & T & T \\ \hline \end{array}$