Non-existence claims making use of the axiom of regularity
13661
Axiom of Regularity allows for this set be an element of itself
84562
Proof using only field axioms
88736
How does the Axiom of Extensionality prove the uniqueness of Specified sets?
53056
natural deduction: introduction of universal quantifier and elimination of existential quantifier explained
20252
The Axiom of Choice and the Cartesian Product.
147874
Why does the existence of independent statements not prove consistency?
38840
Tightness and Inner Regularity
101877
Assumed True until proven False. The Curious Case of the Vacuous Truth
49385
Proving $\forall x (A\to B) \to(A \to \forall x B):x\notin \mbox{free}(A)$ in a Hilbert system where it is not an axiom
35123
How do the separation axioms follow from the replacement axioms?
111723
Can it be proven in $\sf ZF^{\neg\infty}$ that the sets $x_n=\{x_{n+1}\}$ do not exist?
32950
Fake induction proofs
62936
Proving equivalencies of two versions of the Axiom of Choice
106670
Existence of vector space complement and axiom of choice
127114
Differentiability implying continuity
137203
Measurable cardinal existence condition
132532
Things around $(\forall x)(\Psi \Rightarrow \Phi) \Leftrightarrow ((\exists z)\Psi) \Rightarrow \Phi)$