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October Surprise 2024

Simplicify $((A ⇒ B) ⇒ (B ⇒ A)) ⇒( ¬(A∧B) ⇔ ¬(B∨A))$

Rather than defining ∧ ∧ $wedge$ by using $phantom{rule{thickmathspace}{0ex}} phantom{rule{thickmathspace}{0ex}}$, I would define $phantom{rule{thickmathspace}{0ex}} phantom{rule{thickmathspace}{0ex}}$ using ∨ ∨ $vee$, and get rid of all those arrows. Once you have just ¬, ∧ ¬, ∧ $mathrm{neg },wedge$ and ∨ ∨ $vee$, simplification is a bit easier than expressions …