$\forall a[P(a)\implies Q(a)]\wedge \forall a[Q(a)\implies P(a)]\stackrel{?}{\equiv} \forall a[[P(a)\implies Q(a)]\wedge [Q(a)\implies P(a)]]$
46423
Distributivity of quantifiers over logical connectives
111129
Show that $[K:F]_s = [K:L]_s [L:F]_s$ and $[K:F]_i = [K:L]_i [L:F]_i$.
134914
Let $A,B$ and $U$ be sets so that $A\subseteq U$ and $B\subseteq U$. Prove that $A\subseteq B$ iff $(U\setminus B)\subseteq(U\setminus A)$.
65379
Deriving $\neg R$ from $\{R↔(R∨(P∧¬P)), R↔¬P, ¬P→(P↔(Q→Q)), P→Q\}$
80255
How to prove that $|a-b|<\epsilon$ implies $|b|-\epsilon<|a|<|b|+\epsilon$?
83996
For any two sets $A,B$ , $|A|\leq|B|$ or $|B|\leq|A|$
98897
Proving that the set of $\nu$ measurable sets $M\subseteq P(X)$ is an algebra
17624
Axiom of Choice iff Every set has a choice function
47856
$f(x)=ax+b$ for some $a,b\in\mathbb{Q}$ if $f(\mathbb{Q})\subset\mathbb{Q}$ and $f(\mathbb{R-Q})\subseteq \mathbb{R}-\mathbb{Q}$
51369
Natural deduction proof of $p \lor (p\implies q)$ with propositional calculus
151038
How to prove (A v B), (A → C), (B → D) therefore (C v D)
83714
$A \in B$ vs. $A \subset B$ for proofs
70278
$A\subseteq B\to C\setminus B\subseteq C\setminus A\,$ -- how to prove this?
20335
If $A\subset B$ then $\bar{A}\subset \bar{B}$
77297
Counterexample for $A,B\triangleleft G,G/A\cong B \Rightarrow G/B\cong A$
72694
Proving that $f(x) = g(x)$ for some $x \in [a,b]$ if $f,g$ continuous, $f(a)  g(b)$
157924
$\forall x\in\mathbb{N}[(\exists y\in\mathbb{N}(2\leq y\land y<x\land y\ |\ x))\to(\exists z\in\mathbb{N}(2\leq z\land z\leq\sqrt x\land z\ |\ x))]$