One way of getting new true things is really important\. If we know two things are the same, we can always substitute one of them for the other, and this automatically will give us an equality relation between the two things\!

This is sentence is kind of confusing. It seems like it's trying to say that if we know A = B, then we can substitute A for B (or vice versa) and get…. A = B?

It seems like it should say that if A = B, and A occurs in some equation, then we can substitute B in for A in that equation, and the resulting equation will hold.