$Y^\varnothing$ has one element; if $X \ne \varnothing$, then $\varnothing^X = \varnothing$
98470
If $A \ne \varnothing$, then $\varnothing^A=\varnothing$
156443
if $x$ and $y$ commute with $[x y]$, then $[x y]$ is nilpotent
155757
Number theory: $x^y + 1 = y^x$
103801
$xT=x$ iff $x=e$ implies that every $g$ may be written as $x^{-1}(xT)$ for some $x\in G$.
126633
Is a contradiction enough to prove a set equality to $\varnothing$?
146339
Proof of -(-v)=v in a vector space
41364
How to prove that $x^y - y^x = x + y$ has only one solution in positive integers?
125209
Prove $e^x - e^y \leq e |x-y|$ for $x$ belonging to $[0,1]$
46746
How to prove if $u\in W^{1,p}$, then $|u|\in W^{1,p}$?
105367
Proving $||\vec{a}+\vec{b}|| = ||\vec{a}-\vec{b}|| \iff \vec{a} \perp \vec{b}$
74835
how to prove that $ \lim x_n^{y_n}=\lim x_n^{\lim y_n}$?
72920
$x \perp y$ if and only if $\Vert x + \alpha y \Vert \ge \Vert x \Vert$ for all scalars $\alpha$
49240
$\forall x,y \in \mathbb{R}:\vert\cos x- \cos y\vert\leq\vert x-y\vert$
19599
$ d(x_n,y_n) \to d(x,y)$ if $x_n\to x$ and $y_n \to y$
2315
How to prove that $\lVert x + y\rVert = \lVert x\rVert + \lVert y \rVert \implies \lVert tx + (1-t)y\rVert = t\lVert x\rVert + (1-t)\lVert y \rVert$?
105316
Prove : $|x - y| \leqslant \epsilon$ $\forall \epsilon > 0$ iff $x = y$
145600
Is it true that $ U \oplus W_1 = U \oplus W_2 \implies W_1 = W_2 $?