
theorem Th97:
for G being SimpleGraph, x, y being object
 holds not {[x,union G],[y,union G]} in Edges Mycielskian G
proof
let G be SimpleGraph, x, y be object such that
A1: {[x,union G],[y,union G]} in Edges Mycielskian G;
A2: union G in {x,union G} by TARSKI:def 2;
A3: {x,union G} in {{x},{x,union G}} by TARSKI:def 2;
A4: not [x,union G] in union G by A2,A3,XREGULAR:7;
A5: not [x,union G] = union G by A2,TARSKI:def 2;
A6: union G in {y,union G} by TARSKI:def 2;
A7: {y,union G} in {{y},{y,union G}} by TARSKI:def 2;
A8: not [y,union G] in union G by A6,A7,XREGULAR:7;
A9: not [y,union G] = union G by A6,TARSKI:def 2;
   {[x,union G],[y,union G]} in Edges G by A1,A4,A5,A8,A9,Th93;
 hence contradiction by A4,Th13;
end;
