How can I create a vertical line in a math block with alignment points?

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$& Rho(T sect G) &= Rho(T|G) dot Rho(G) \
    + &Rho(T sect B) &= Rho(T|B) dot Rho(B) \
    + &Rho(T sect R) &= Rho(T|R) dot Rho(R) \
    #place(line(length: 5cm, stroke: 0.05em), dy: -3.4mm)
    & Rho(T)$

asdf

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