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  "body": "\n## Summary\n\nA Pixley term of a [[variety|AJNZJD8442]] is a ternary term $p$ such that $p(x, y, y) = x$, $p(x, x, y) = y$ and $p(x, y, x) = x$ hold.\nBy Pixley's theorem, a variety has a Pixley term if and only if it is an [[arithmetical variety|GW78A05TNA]].\nA Pixley term is a [[Mal'cev term|Y203PPTS61]] that also yields a [[majority term|9879ZMW5AA]].\n\n## Explanations\n\n### L1 human\n\nA Pixley term is a three-input formula that behaves like the Mal'cev term of groups, and in addition returns $x$ on inputs $x, y, x$.\nFor Boolean algebras it can be written with \"and\", \"or\" and \"not\".\nIts existence makes the congruences of every algebra in the variety both permute and satisfy the distributive law.\n",
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