SPFL chief executive Neil Doncaster feels the governing body have been given a "very clear mandate" after calls for an inquiry were voted down.
Rangers had put forward a resolution for an independent inquiry into the handling of a vote to end the lower leagues, which could also see the Premiership declared over on a points-per-game basis.
With Hearts and Stranraer backing their calls for an emergency general meeting a ballot was held on Tuesday, but just 13 of the 42 clubs backed the call.
Rangers had called for the chief executive and legal advisor Rod McKenzie to be suspended but failed to achieve the necessary support for their proposal.
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