Why Cook-Levin thorem's proof can mean SAT's NP-Hardness
Any language&nbsp;$L$ in NP is decided by some nondeterministic Turing machine&nbsp;$M$. By Cook&ndash;Levin, the problem "Does $M$ accept input&nbsp;$x$?" can be decided by constructing a Boolean formula $\varphi_{M,x}$ that is satisfiable if, and only if, $M$ accepts&nbsp;$x$. Hence $L$&nbsp;reduces to SAT, so SAT is NP-hard.