‘We thus proposed that a pre-exposure covariate C be considered a confounder for the effect of A on Y if there exists a set of covariates X such that the effect of the exposure on the outcome is unconfounded conditional on (X, C) but for no proper subset of (X, C) is the effect of the exposure on the outcome unconfounded given the subset.’ (VanderWeele & Shpitser, 2013, p. 215)
VanderWeele, T. J., & Shpitser, I. (2013). On the definition of a confounder. The Annals of Statistics, 41(1), 196–220.