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We derive and apply a general scheme for mapping a setup consisting of ahalf-filled single level quantum dot coupled to one normal metallic and twosuperconducting phase-biased leads onto an ordinary half-filled single impurityAnderson model with single modified tunneling density of states. The theoryallows for the otherwise unfeasible application of the standard numericalrenormalization group and enables to obtain phase-dependent local spectralproperties as well as phase-dependent induced pairing and Josephson current.The resulting transport properties match well with the numerically exactcontinuous-time hybridization-expansion quantum Monte Carlo. For weakly couplednormal electrode, the spectral properties can be interpreted in terms ofnormal-electrode-broadened Andreev bound states with phase-dependent positionanalogous to the superconducting Anderson model, which coexist in the$\pi$-like phase with a Kondo peak whose phase-dependent Kondo temperaturefollows the form conjectured previously in Doma\'nski et al., Phys.~Rev.~B {\bf95}, 045104 (2017)

Spectral and transport properties of a half-filled Anderson impurity coupled to phase-biased superconducting and metallic leads