1. Proof steps: (Take proving that P is equivalent to Q as an example)

Step 1: Prove sufficiency (that is, prove "if P, then Q")

Step 2: Prove the necessity (that is, prove "if Q, then P")

According to the first two steps, it can be explained that p is equivalent to Q.

2. There are many equivalence proofs, such as vector equivalence proof, matrix equivalence proof, rational number equivalence proof, computer formula equivalence proof, and the most important thing is to follow the commodity steps.