Here is a model write-up of a proof that a given sentence is a theorem, giving each step along with detailed reasons for that step. You should aim to copy this style in your assignments.
Here we prove that .
Since we know , then by transitivity once, and so by equanimity we have that . QED.
You can always write ``A is a theorem'' instead of if you wish.
This should be on a different page, but running latex2html is not that easy, so I thought it best to put it here...
Remember that I had a problem with proving one step of Theorem 3.32 - here it is corrected.