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This paper deals with the identification problem of causal effects in randomized trials with noncompliance. In this problem, generally, causal effects are not identifiable and thus have been evaluated under some strict assumptions, or through the bounds. Different from existing studies, we propose novel identification conditions of joint probabilities of potential outcomes, which allow us to derive a consistent estimator of the causal effect. Regarding the identification conditions of joint probabilities of potential outcomes, the assumptions of monotonicity (Pearl, 2009), independence between potential outcomes (Robins & Richardson, 2011), gain equality (Li & Pearl, 2019) and specific functional relationships between cause and effect (Pearl, 2009) have been utilized. In contrast, without such assumptions, the proposed conditions enable us to evaluate joint probabilities of potential outcomes using an instrumental variable and a proxy variable of potential outcomes. The results of this paper extend the range of solvable identification problems in causal inference.