picture showing elimination and intro rules for implication

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   rzeta0 (rzeta0@mastodon.social)'s status on Saturday, 28-Jun-2025 05:53:41 JST rzeta0

   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