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Opamp floating supplies and ground reference

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op amp floating

A question about general opamps (see attached picture):

Normally, with regular power supplies, the macro model of an ideal opamp can be shown to be the picture in the top (notice that the output voltage is referenced to ground).

==> Consider the bottom opamp model and macro model. If I leave the power supplies of the opamp floating (no ground reference), does the opamp output become differential (floating)?
 

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