reserve p1,p2,p3,p4,p5,p6,p,pc for Point of TOP-REAL 2;
reserve a,b,c,r,s for Real;

theorem Th24:
  p1,p2,p3 are_mutually_distinct & angle(p1,p2,p3)>PI implies
  angle(p2,p3,p1)>PI & angle(p3,p1,p2)>PI
proof
  assume
A1: p1,p2,p3 are_mutually_distinct;
  then
A2: p1<>p2 & p1<>p3 by ZFMISC_1:def 5;
  assume
A3: angle(p1,p2,p3)>PI;
A4: p2<>p3 by A1,ZFMISC_1:def 5;
  then p2,p3,p1 are_mutually_distinct by A2,ZFMISC_1:def 5;
  hence angle(p2,p3,p1)>PI by A3,Th23;
  p3,p1,p2 are_mutually_distinct by A2,A4,ZFMISC_1:def 5;
  hence thesis by A3,Th23;
end;
