I'm presented with a Hilbert system with just one inference rule (MP) and these axiom schemes:
$$A \supset (B \supset A)$$ $$(A \supset (B \supset C)) \supset ((A \supset B) \supset (A \supset C))$$ $$A \supset (B \supset A \wedge B)$$ $$A \wedge B \supset A$$ $$A \wedge B \supset B$$ $$(A \supset C) \supset ((B \supset C) \supset (A \vee B \supset C))$$ $$A \supset A \vee B$$ $$B \supset A \vee B$$ $$(A \supset B) \supset ((A \supset \neg B) \supset \neg A)$$ $$\neg \neg A \supset A$$ $$\textbf{F} \supset A$$ $$A \supset \textbf{T}$$
How am I supposed to memorize all of them? In other words, why these particular schemes? I think I've seen examples of every one of them to be necessary for various formal proofs, but I'm curious how the authors have come up with this.