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Need some help.

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I know that to prove P ⇒ Q, I assume P and derive Q.

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Now to prove

(A⇒B) ⇒ ((B⇒C) ⇒ (A⇒C))

I need to assume (A⇒B) and derive ((B⇒C) ⇒ (A⇒C)).

But I can't seem to make progress from (A⇒B) alone, I think I need to assume A is true as well.

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Intuitively the statement makes total sense. But drawing the derivation as per image attached using elim and intro rules, I get stuck unless I assume A too.

Can anyone help clarify my thinking?

#maths #cs #logic