Non-causality: The role of the omitted variables

In this paper a proof is offered that if a variable Y3 does not cause a variable Y1 in the bivariate system (Y1, Y3) and Y3 causes a variable Y1 in higher-order system (Y1, Y2, Y3), then the omitted variable Y2 must cause the variable Y1 in the bivariate system (Y1, Y2) and in the trivariate system (Y1, Y2, Y3).