Factor Principles/Conjunction on Right/Formulation 1/Proof by Truth Table

Theorem

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

Proof
Proof by Truth Table.

$\begin{array}{ccc||ccccccccccc} p & q & r & (p & \implies & q) & \implies & ((p & \land & r) & \implies & (q & \land & r)) \\ \hline T & T & T & T & T & T & T & T & T & T & T & T & T & T\\ T & T & F & T & T & T & T & T & F & F & T & T & F & F\\ T & F & T & T & F & F & T & T & T & T & F & F & F & T\\ T & F & F & T & F & F & T & T & F & F & T & F & F & F\\ F & T & T & F & T & T & T & F & F & T & T & T & T & T\\ F & T & F & F & T & T & T & F & F & F & T & T & F & F\\ F & F & T & F & T & F & T & F & F & T & T & F & F & T\\ F & F & F & F & T & F & T & F & F & F & T & F & F & F\\ \end{array}$