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We prove that if $\\mathcal{P}$ is $d_{1}$-connected and $\\mathcal{Q}$ is $d_{2}$-connected, then their Boardman-Vogt tensor product $\\mathcal{P}\\otimes\\mathcal{Q}$ is $\\left(d_{1}+d_{2}+2\\right)$-connected. 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Let $\\mathcal{P}$ and $\\mathcal{Q}$ be two reduced $\\infty$-operads. We prove that if $\\mathcal{P}$ is $d_{1}$-connected and $\\mathcal{Q}$ is $d_{2}$-connected, then their Boardman-Vogt tensor product $\\mathcal{P}\\otimes\\mathcal{Q}$ is $\\left(d_{1}+d_{2}+2\\right)$-connected. 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