Given the premises p→q and ¬p→¬q, prove that p is logically equivalent to q Given the premises p→q and ¬p→¬q, prove that p is logically equivalent to q.
I understand why this works, but I do not know how to construct a complete formal proof. So far, I have this:
premises:
p→q ¬p→¬q 
(p→q) ∧ (¬p→¬q) ⇔ T
apply contrapositive law
(p→q) ∧ (q→p) ⇔ T
∴ (p↔q) ⇔ T

At this point, how do I formally assert (using symbols and laws) that, because (p↔q) is a tautology, p and q must be logically equivalent to each other?

$p$ and $q$ are of course not logically equivalent. However, you can derive the truth of $p \leftrightarrow q$ from those two premises ... which is probably what you are really asked to do.
