Two statements are equivalent if... Two statements "If A, then B." and "If P, then R." are equivalent if the validity of one statement implies the validity of the other?
That is, I assume that "If A, then B." is valid, then proceed to show the second statement is valid, and vice versa?
Or this done differently?
To show that a statement is valid, one need only show that if the premise is true, the conclusion necessarily follows, right?


Two statements "If A, then B." and "If P, then R." are equivalent if the validity of one statement implies the validity of the other?

Not quite right.  It's not the the validity of the one statement implies the other (and vice versa), but rather that the assumed truth of the one implies the other (and vice versa)

That is, I assume that "If A, then B." is valid, then proceed to show the second statement is valid, and vice versa?

OK, so here's an example of what I mean.  By itself, $A \to B$ is not valid. So, anything would follow once you assume it is valid, which includes something like the validity of $C$. That is, by your proposed definition, the validity of $C$ folows from the validity of $A \to B$. But, clearly $C$ is not implied by $A \to B$, let alone that it would be equivalent to it.
So, you have to think about this in terms of the truth of the statements, rather than their validity: if you assume the $A \to B$ is true, does it mean that $C$ has to be true as well? No. So, $A \to B$ does not imply $C$ ... which is of course exactly what we want.
If you do want to talk about validity, you can do the following:
Two statements $\phi$ and $\psi$ are equivalent if and only if the inference from $\phi$ to $\psi$ is logically valid, and vice versa. Or: if the statements $\phi \to \psi$ and $\psi \to \phi$ are both valid.
