Inexpressibility of $\vee$ in term of $\wedge, \to$ and $\bot$ in intuitionistic logic.
42869
Is $\lor$ definable in intuitionistic logic?
20556
Isomorphism between two models of Hilbert's Axioms with different notions of congruence
150385
The use of the Axiom of Choice in this proof of the sequence lemma
122184
De Morgan's laws in logic and set theory
6535
Proof of for-all / there-exists "negation"?
79328
Proposition 5.15 from Atiyah and Macdonald: Integral Closure and Minimal Polynomial
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
94771
Not every boolean function is constructed from $\wedge$ (and) and $\vee$ (or)
155266
Is $\exp:\overline{\mathbb{M}}_n\to\mathbb{M}_n$ injective?
65910
Reflexivity of equivalence relations
103112
Does the existential quantifier distribute over an implication?
118189
Proving the pairing axiom from the rest of ZF
85398
$\mathsf{ZF}$ is not finitely axiomatizable
157924
$\forall x\in\mathbb{N}[(\exists y\in\mathbb{N}(2\leq y\land y<x\land y\ |\ x))\to(\exists z\in\mathbb{N}(2\leq z\land z\leq\sqrt x\land z\ |\ x))]$
126870
Show that axiom of replacement implies from the Axiom of Specification [Proof Verification]
154363
Prove that $\text{aff}(X) = \text{aff}(\text{closure}(X))$
93342
Show that $\neg$ and $\wedge$ form a functionally complete collection of logical operators.