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In this note we present a second independent proof for the theorem introducedpreviously that establishes an isomorphism between SU(2) and LB1 X LB1 X LB1.Since the local groups LB1 and LB2 are isomorphic, it was also previouslyproved a similar result for LB2 X LB2 X LB2. We are going to reverse the threesets of tetrads that are going to be used in order to prove this new version.Instead of choosing three SU(2) different tetrads keeping the electromagnetictetrad the same for all three sets of SU(2) tetrads, we are going to keep fixedthe SU(2) tetrad, that is, we are going to pick just one SU(2) tetrad butchoose three different arbitrary but fixed electromagnetic tetrads in order togauge locally the only local SU(2) tetrad involved in our new version of thistheorem. The same result will be obtained via an alternative but equivalentway.

Second proof for SU(2) isomorphic to LB1 X LB1 X LB1 theorem