let A, B be complex-membered set ; :: thesis: for a being complex number st a -- A = a -- B holds
A = B
let a be complex number ; :: thesis: ( a -- A = a -- B implies A = B )
assume a -- A = a -- B ; :: thesis: A = B
then ( A c= B & B c= A ) by Th169;
hence A = B by XBOOLE_0:def 10; :: thesis: verum