Prove propositional formula is a tautology I need to show this formula is a theorem of propositional calculus. I tried assuming antecedent and proving consequent but didn't work for this proof. Do I need to show it is equivalent to true? How should I start? It's not possible to use truth tables.

$(p \rightarrow q) \rightarrow (p \wedge r \rightarrow q \wedge r)$

Background:

In my class, there is no mention to it but I think this form of logic it's called Equational Logic.
Probably, it's based on this book: A Logical Approach to Discrete Math
by David Gries

EDIT:
I was asked to provide more details on the type of proof needed. In my class, I am not allowed to use truth tables to prove this proposition. This is an example:
Here is what the formula states:


  If $p$ implies $q$, then $p$ and $r$ imply $q$ and $r$.


To prove this, you would like to argue as follows. Assume $p$ implies $q$, and suppose that both $p$ and $r$ hold. Since $p$ implies $q$, then $q$ holds. Hence both $q$ and $r$ hold.

How exactly this proof is expressed depends on your proof system.