Is the axiom of regularity/foundation equivalent to $\forall x:x\notin x$?
120311
Equivalence of Axiom of Regularity
155136
$x\in \{\{\{x\}\}\}$ or not?
155618
Slightly changing the formal definition of continuity of $f: \mathbb{R} \to \mathbb{R}$?
47637
Are strict local minima of a general function always countable?
6535
Proof of for-all / there-exists "negation"?
132532
Things around $(\forall x)(\Psi \Rightarrow \Phi) \Leftrightarrow ((\exists z)\Psi) \Rightarrow \Phi)$
83757
Is the following equivalent to the axiom of choice?
144899
Do We Need the Axiom of Choice for Finite Sets?
153935
A weaker Axiom of Infinity?
20437
Closed surjection that does not preserve regularity
31389
consistency of ZF\{Power Set axiom}
42150
Prove that $\forall x \neg P(x) \iff \neg \exists x P(x)$
65308
Axiom of Choice: Family of non-empty sets mutually disjoint or not?
21202
Axiom of choice is equivalent to every relation includes a function with the same domain
90055
Show that $\mathcal P(x)\notin x$
78290
Countable axiom of choice: why you can't prove it from just ZF
106284
Establishing a Basis for $F[x]/(f(x))$