Magic system

Rough exemplary ideas for set theory in first-order logic

Symbols Magic Ingredients
Variables ???
\(\in\) ???
sets \(\{ x \mid \varphi (x) \}\) ???
functions ???
relations ???
Quantifiers (binding agents - weak (\(\exists\)) and strong (\(\forall\))? )
\(\wedge\) fusing two ingredients
\(\to\) ???
\(\neg\) anti-ingredient (fusing an ingredient with its anti-ingredient will blow up in your face, unless carefully controlled (proof by contradiction))
Sentences Magic spells
???
Proving Sentences Learning Spells
proof steps / techniques gestures / magic words

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