The question:
Prove that if A ~ B then B ~ A
My attempt:
1.
2.
Sub 1 into 2:
Let S = I
Thus A = A, and similarly B = B. Which is true. I'm pretty sure this isn't the correct process. What should I be doing to prove this? Thanks.
Yes, this is invalid. You have essentially shown that if you assume what you want to prove, you arrive at a true statement. That is not a valid proof method.
(You will sometimes see what is called "synthetic proof" where you start from the thing you want to prove and show the hypotheses. That is valid only if every step is "invertible". Then you could use reverse the proof and go from the hypotheses to the conclusion. That is the real proof. In a "synthetic proof" that reverse should be so obvious you don't have to explicitely do it.)
As both Obd2 and FernandoRevilla has said, you can go from to by taking .