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Solve with the assumption z!=0

When I try to solve the following with the assumption z is nonzero solve still outputs the solution with z=0:

assume(z!=0)
solve([x,y*z],x,y,z,solution_dict=True)

Output:

[{x: 0, y: r79, z: 0}, {x: 0, y: 0, z: r80}]