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  "body": "\n## Statement\n\nLet $A$ and $B$ be [[sets|0SJ3RX9TXA]].\nIf $A$ and $B$ have the same [[elements|0EZ758XE73]], then $A = B$:\n$$\\forall A \\, \\forall B \\, \\bigl( \\forall x \\, (x \\in A \\leftrightarrow x \\in B) \\to A = B \\bigr).$$\n\n## Remarks\n\nIt is one of the axioms of [[Zermelo–Fraenkel set theory|0HE5WDQ9FJ]].\nThe converse is a rule of logic: equal sets have the same elements.\nIn practice, $A = B$ is often proved with $A \\subseteq B$ and $B \\subseteq A$. See [[subset|0FE8Q5S42Y]].\n\n## Explanations\n\n### L1 human\n\nA set is nothing more than its elements.\nIf two sets contain exactly the same things, they are the same set, however you describe them.\nFor example, $\\{x \\in \\mathbb{R} \\mid x^2 = 1\\}$ and $\\{-1, 1\\}$ are equal.\n",
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