The EC also told Justice Bela Trivedi that under The Representation of The People Act, it cannot be made a respondent to the petition filed by BJP's Balwantsinh Rajput, who demanded that Ahmed Patel's election be set aside.
Irani, Shah and Ahmed Patel had won the closely contested election.
The EC, which has been made a party to the petition along with the three winning candidates, said in its reply it stands by its order.
The court adjourned the hearing to November 10.
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Ahmed Patel, in his reply filed last week, had sought dismissal of the petition, claiming that there was no substance in the allegations.
Rajput had quit the Congress just ahead of the August 8 Rajya Sabha election for three seats from Gujarat, and was fielded as a BJP candidate along with Shah and Irani.
Rajput, however, lost to Congress's Ahmed Patel as the EC rejected the votes of rebel Congress MLAs Raghavjee Patel and Bholabhai Gohel for flouting rules.
Both the rebel MLAs voted for BJP candidate Rajput, instead of Ahmed Patel. With these two votes getting invalidated, the Congress leader trumped Rajput.
Rajput alleged in his petition that the EC order was "patently illegal".
He also claimed that two other Congress MLAs had flouted the same rule by showing their ballot papers to unauthorised persons, so their votes should be invalidated, and he (Rajput) be declared winner.