let E, x be set ; :: thesis: for A being Subset of (E ^omega) holds
( <%x%> in A ? iff <%x%> in A )
let A be Subset of (E ^omega); :: thesis: ( <%x%> in A ? iff <%x%> in A )
A ? = A |^ (0,1) by Th79;
hence ( <%x%> in A ? iff <%x%> in A ) by Th53; :: thesis: verum