Bell inverted the EPR argument since EPR had used locality as an assumption - Bell's theorem converted EPR's local-realist position into a paradigm of what is not true.

Bell's ingenious proof focused on EPResque 2-particle systems: pairs which are perfectly correlated along any given measurement axis - recall that EPR had taken this correlation as implying underlying variables, but Bell problematized this conclusion by examining some other similar correlations of the pairs: for example when measured along respective axes with a relative rotation though some angle...

With a relative angle between them the correlation between the two measurements is no longer perfect but varies as the cosine of the angle. Bell explored the type of underlying variable models (with built in locality) which EPR had suggested, and showed that the entire class of such models could in this case not give the same cosine varying correlation as quantum theory predicted.

Generally, the quantum correlations are "stronger" than the limit possible for local hidden variable theories.

In 1991 GHZ sharpened Bell's result by considering systems of three or more particles and deriving an outright contradiction among EPR's assumptions.

Quantum theory "looks" nonlocal (e.g. I measure here and collapse everywhere) and Bell's theorem seems to resolve the question in the affirmative. In the language of wavefunction collapse, Bell-GHZ showed that wavefunctions "collapse at a distance" as surely as they do locally.