Proof by ………..uses the equivalence p →q≡ ~q→~p.

The proof method that uses the equivalence p →q≡ ~q→~p is called "Proof by Contrapositive".

Here are the steps to use this method:

1. Assume that the statement p → q is true. This means that if p is true, then q must also be true.

2. The contrapositive of this statement is ~q → ~p. This means that if q is not true (denoted by ~q), then p is not true (denoted by ~p).

3. If you can prove that ~q → ~p is true, then you have proven that p → q is true, because they are logically equivalent. This is the basis of proof by contrapositive.

4. To use this method, you would start by assuming ~q is true, and then try to logically deduce that ~p must also be true.

5. If you can do this, then you have proven the original statement p → q by contrapositive.