:: deftheorem Def1 defines ComplexSubAlgebra CC0SP1:def 1 :
for V, b₂ being ComplexAlgebra holds
( b₂ is ComplexSubAlgebra of V iff ( the carrier of b₂ c= the carrier of V & the addF of b₂ = the addF of V || the carrier of b₂ & the multF of b₂ = the multF of V || the carrier of b₂ & the Mult of b₂ = the Mult of V | [:COMPLEX, the carrier of b₂:] & 1. b₂ = 1. V & 0. b₂ = 0. V ) );