$ \forall x ( P(x) \lor Q(x)) \iff \forall x (P(x)) \lor \forall x (Q(x) ) $
59187
Proof, is $\forall x : (P(x) \lor Q(x)) \Leftrightarrow \forall x : P(x) \lor \forall x : Q(x)$?
79969
Proof that a formula $\theta$ is valid if and only if $\forall x \theta$ is valid
102943
$f(x)=1/q$ for $x=p/q$ is integrable
28007
Assuming: $\forall x \in [0,1]:f(x) > x$ Prove: $\forall x \in [0,1]:f(x) > x + \varepsilon $
70117
Show that $(p \to q) \lor (q \to p)$ is a tautology
88201
Suppose $X$ is a finite set and $f : X \to X$ is a function. Then $f$ is injective if and only if $f$ is surjective.
47856
$f(x)=ax+b$ for some $a,b\in\mathbb{Q}$ if $f(\mathbb{Q})\subset\mathbb{Q}$ and $f(\mathbb{R-Q})\subseteq \mathbb{R}-\mathbb{Q}$
139537
Show that $x\subseteq y \Leftrightarrow \mathcal{P}(x)\subseteq\mathcal{P}(y)$.
25187
Why $∀x(P(x)→Q)$ is equivalent to $∃xP(x)→Q$
144693
Show that if $B \subseteq C$, then $\mathcal{P}(B) \subseteq \mathcal{P}(C)$
130998
Is $\exists x \in A ~:~ P(x)$ the same as $\exists x ~:~ x \in A \implies P(x)$
13732
$||f||_p\to ||f||_\infty$ under general assumptions
79407
How to solve ~(P → Q) : P & ~Q by natural deduction?
157625
How to prove conditional in Coq?
67709
Stuck with proof for $\forall A\forall B(\mathcal{P}(A)\cup\mathcal{P}(B)=\mathcal{P}(A\cup B)\rightarrow A\subseteq B \vee B\subseteq A)$
29031
How does "If $P$ then $Q$" have the same meaning as "$Q$ only if $P$ "?
34768
Proving $(p \oplus q) \oplus r=p \oplus (q \oplus r)$