In this paper, we propose a novel relay selection scheme for orthogonal frequency-division multiplexing (OFDM) systems by combining conventional bulk and per-subcarrier selection schemes, and analyze its outage performance over equally spatially correlated channels. Specifically, the combined selection scheme selects only two relays at the first attempt and performs per-subcarrier selection over these two relays. We analyze the asymptotic outage performance of the combined selection scheme in the high signal-to-noise (SNR) region, and prove a generalized theorem. This theorem states that the combined selection can achieve an optimal outage probability equivalent to the persubcarrier selection at high SNR without using the full set of available relays for selection. This unique property is termed the equivalence principle, and it holds for all correlation conditions. To explore this principle, we consider three examples: decodeand-forward (DF), fixed-gain (FG) amplify-and-forward (AF) and variable-gain (VG) AF relay systems. Furthermore, two extended applications, antenna selection and branch selection, are also considered to reveal the feasibility and the expandability of the equivalence principle. Our analysis is verified by Monte Carlo simulations. The proposed combined selection and the proved theorem provide a general and feasible solution to the trade-off between system complexity and outage performance when relay selection is applied.