let A, B be complex-membered set ; :: thesis: for a being Complex st a <> 0 & a /// A = a /// B holds
A = B
let a be Complex; :: thesis: ( a <> 0 & a /// A = a /// B implies A = B )
assume ( a <> 0 & a /// A = a /// B ) ; :: thesis: A = B
then ( A c= B & B c= A ) by Th216;
hence A = B ; :: thesis: verum