How to test for Granger causality?

I am trying to test if $a_t$ granger causes $b_t$:

$$a_t=rho_1+phi_{11}a_{t-1}+alpha_{11}b_{t-1}+beta_{11}c_{t-1}+u_{1t}$$

$$b_t=rho_2+phi_{21}a_{t-1}+alpha_{21}b_{t-1}+beta_{21}c_{t-1}+u_{2t}$$

$$c_t=rho_3+phi_{31}a_{t-1}+alpha_{31}b_{t-1}+phi_{31}c_{t-1}+u_{3t}$$

I am trying to use an F test.

However, should be null be: $phi_{21}$ = 0.

Or do I also need to set: $beta_{21}$ = 0 because a impacts b through c.