Question: Can I plot3d with an condition?

I would like to look at a 3d plot including an condition about the tree variables of the plot

For this simple case, I only want to see the plot with the condition that 
{40 < y, x < y-40, z < y-40} or {x = 0, y = 40, z <= 0}, {y = x+40, 0 < x, z < x}, {y = x+40, z = x, 0 < x}

. Is that possible? 

In 2d there is no problem. And in 3d I do not know how.

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