Previously it has been shown that do-calculus is a sound inferential machinery for estimating a causal effect from a causal diagram and a set of observations and interventions. This paper further proves that it is not only sound, but also complete, meaning that every valid equality between probabilities defined on a semi-Markovian graph can be obtained through finite applications of the three rules of do-calculus. Moreover, the paper studies mz-transportability, which unifies those previously studied special cases of meta-identifiability. The authors proposed a complete algorithm to determine if a causal effect is mz-transportable, and if it is, outputs a transport formula for estimating the causal effect.