  Quantum nonlocality has recently been classified into three distinct types:
quantum entanglement, Einstein-Podolsky-Rosen (EPR) steering, and Bell's
nonlocality. Experimentally Bell's nonlocality is usually tested by quantum
violation of the Clause-Horne-Shimony-Holt (CHSH) inequality in the two-qubit
system. Bell's nonlocality is the strongest type of nonlocality, also due this
reason Bell-test experiments have encountered both the locality loophole and
the detection loophole for a very long time. As a weaker nonlocality, EPR
steering naturally escapes from the locality loophole and is correspondingly
easier to be demonstrated without the detection loophole. In this work, we
trigger an extraordinary approach to investigate Bell's nonlocality, which is
strongly based on the EPR steering. We present a theorem, showing that for any
two-qubit state $\tau$, if its mapped state $\rho$ is EPR steerable, then the
state $\tau$ must be Bell nonlocal. The result not only pinpoints a deep
connection between EPR steering and Bell's nonlocality, but also sheds a new
light to realize a loophole-free Bell-test experiment (without the CHSH
inequality) through the violation of steering inequality.
