Kind of. Basically the smaller explosion forces the nuclear material, say, uranium, together to create nuclear fission, which causes a massive release of energy. Since that's all explosions are, a release of energy.
So, the very first nuclear weapon worked like this...
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So, the very first nuclear weapon worked like this...
(EXPLOSVE-(U235)=====)U235)
(BOOM!==(U235=>==)U235)
Then a nuclear explosion.