If $Z[J]$ is the generating functional for the path-integral, could any prove (or more reasonably, refer me to a proof) that $W[J]\equiv-i\log\left(Z[J]\right)$ "generates" only connected diagrams?

So far I've only seen theory-dependent "examples" (basically showing how in $\phi^4$ theory the two-point function from $W$ gives only connected contributions).

I'm looking for a generic systematic proof for a general field theory.

If $Z[J]$ is the generating functional for the path-integral, could any prove (or more reasonably, refer me to a proof) that $$W[J]\equiv\frac{\hbar}{i}\log\left(Z[J]\right)$$ "generates" only connected diagrams?

So far I've only seen theory-dependent "examples" (basically showing how in $\phi^4$ theory the two-point function from $W$ gives only connected contributions).

I'm looking for a generic systematic proof for a general field theory.