Formal proof of the statement $\exists x \forall y: R(x,y) \implies \forall y \exists x: R(x, y)$
15354
Formal proof of $\exists x \forall y P(x,y) \implies \forall y \exists x P(x,y)$
139537
Show that $x\subseteq y \Leftrightarrow \mathcal{P}(x)\subseteq\mathcal{P}(y)$.
22232
Proving that cardinality of the reals = cardinality of $[0,1]$
116056
Prove that $|f(x)-f(y)|\le|x-y|$ for all $x$ and $y$.
58186
Set theory proof, $\exists g(g\colon A\twoheadrightarrow C)$ or $\exists h(h\colon C\hookrightarrow B)$
138897
help with some Hilbert style proofs in a propositional logic axiom system.
114608
Proof concerning regular space: there exist a closed set contained in any open set containing $x$
133884
A proof using Yoneda lemma
151935
Proving the predicate $\forall n \in \mathbb{N} , n \geq 2$ using the Pigeonhole principle
70166
Why is the universal quantifier $\forall x \in A : P(x)$ defined as $\forall x (x \in A \implies P(x))$ using an implication?
49240
$\forall x,y \in \mathbb{R}:\vert\cos x- \cos y\vert\leq\vert x-y\vert$
57215
Stuck on formal proofs. Not sure how to continue
1821
Proving $f(C) \setminus f(D) \subseteq f(C \setminus D)$ and disproving equality
75007
How can I prove this relation between the elementary set theory and the elementary logic?
9282
Prove using natural deduction $((P \land Q) \rightarrow R) \vdash (P \rightarrow R) \lor (Q\rightarrow R)$
126870
Show that axiom of replacement implies from the Axiom of Specification [Proof Verification]
56351
Prove that these statements $(A \lor \neg B)$ and $\neg A \to \neg B$ are logically equivalent