2-local triple homomorphisms on von Neumann algebras and JBW⁎-triples

We prove that every (not necessarily linear nor continuous) 2-local triple homomorphism from a JBW⁎-triple into a JB⁎-triple is linear and a triple homomorphism. Consequently, every 2-local triple homomorphism from a von Neumann algebra (respectively, from a JBW⁎-algebra) into a C⁎-algebra (respectively, into a JB⁎-algebra) is linear and a triple homomorphism.