Also, in universal algebra, a variety is a class of algebraic structures that share the same operations, and the same axioms, with the condition that all axioms are identities. What precedes shows that existential axioms of the above form are accepted in the definition of a variety.
also, in UnivERsaL algEbra, A vAriEty IS a class of ALGebrAic strUCTUres thaT sharE thE saMe operAtIoNS, aNd the same axioms, WiTh THe COnDiTion tHat alL axioms ARe ideNtitiEs. whAt preCedes showS thAT ExisteNtIal axiOms OF THe above Form aRe AcCeptED in the DEfIniTion Of A vaRIety.