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If $T$ is a bilinear bi-parameter singular integral satisfying suitable $T1$ type assumptions, $\\|b\\|_{\\operatorname{bmo}(\\mathbb{R}^{n+m})} = 1$ and $1 < p, q \\le \\infty$ and $1/2 < r < \\infty$ satisfy $1/p+1/q = 1/r$, then we have $$ \\|[b, T]_1(f_1, f_2)\\|_{L^r(\\mathbb{R}^{n+m})} \\lesssim \\|f_1\\|_{L^p(\\mathbb{R}^{n+m})} \\|f_2\\|_{L^q(\\mathbb{R}^{n+m})}. $$ Previously the range $r \\le 1$ was proved only in the paraproduct free situation. 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