Theorems with one-line proofs

A famous one : Irrational number to an irrational power can be rational.

Proof : If $\sqrt 2^{\sqrt 2}$ is rational, we are happy. If $\sqrt 2^\sqrt 2$ is irrational, then $(\sqrt 2^{\sqrt 2})^\sqrt 2=2$ is rational.

P.S. $\sqrt 2^\sqrt 2$ is actually irrational because it is transcendental by Gelfond–Schneider theorem, but we don't need to know this theorem to prove the above statement.

Hairy Ball theorem (for $n=2$): There are no non-vanishing continuous tangent vector field for $S^2$

Proof:: If such a vector field did exist, let $v_x$ be the vector at $x$. The function $H:S^2 \times [0,1] \to S^2$ mapping $(x,t)$ to the point $t\pi$ radians away from $x$ along the great circle defined by $v_x$ is a homotopy between the identity and the antipodal map on $S^2$, which is impossible.

Well I wrote two sentences, but essentially it is one.