  Einstein-Podolsky-Rosen steering is a form of quantum nonlocality
intermediate between entanglement and Bell nonlocality. Although Schr\"odinger
already mooted the idea in 1935, steering still defies a complete
understanding. In analogy to "all-versus-nothing" proofs of Bell nonlocality,
here we present a proof of steering without inequalities rendering the
detection of correlations leading to a violation of steering inequalities
unnecessary. We show that, given any two-qubit entangled state, the existence
of certain projective measurement by Alice so that Bob's normalized conditional
states can be regarded as two different pure states provides a criterion for
Alice-to-Bob steerability. A steering inequality equivalent to the
all-versus-nothing proof is also obtained. Our result clearly demonstrates that
there exist many quantum states which do not violate any previously known
steering inequality but are indeed steerable. Our method offers advantages over
the existing methods for experimentally testing steerability, and sheds new
light on the asymmetric steering problem.
