reserve x1, x2, x3, x4, x5, x6, x7 for set;

theorem
  x1, x2, x3, x4, x5, x6, x7 are_mutually_distinct implies x1, x2, x5,
  x3, x6, x7, x4 are_mutually_distinct
proof
  assume
A1: x1, x2, x3, x4, x5, x6, x7 are_mutually_distinct;
  then
A2: x1 <> x3 by ZFMISC_1:def 9;
A3: x5 <> x7 by A1,ZFMISC_1:def 9;
A4: x5 <> x6 by A1,ZFMISC_1:def 9;
A5: x4 <> x7 by A1,ZFMISC_1:def 9;
A6: x4 <> x6 by A1,ZFMISC_1:def 9;
A7: x6 <> x7 by A1,ZFMISC_1:def 9;
A8: x1 <> x5 by A1,ZFMISC_1:def 9;
A9: x1 <> x4 by A1,ZFMISC_1:def 9;
A10: x2 <> x4 by A1,ZFMISC_1:def 9;
A11: x2 <> x3 by A1,ZFMISC_1:def 9;
A12: x1 <> x7 by A1,ZFMISC_1:def 9;
A13: x1 <> x6 by A1,ZFMISC_1:def 9;
A14: x4 <> x5 by A1,ZFMISC_1:def 9;
A15: x3 <> x7 by A1,ZFMISC_1:def 9;
A16: x3 <> x6 by A1,ZFMISC_1:def 9;
A17: x3 <> x5 by A1,ZFMISC_1:def 9;
A18: x3 <> x4 by A1,ZFMISC_1:def 9;
A19: x2 <> x7 by A1,ZFMISC_1:def 9;
A20: x2 <> x6 by A1,ZFMISC_1:def 9;
A21: x2 <> x5 by A1,ZFMISC_1:def 9;
  x1 <> x2 by A1,ZFMISC_1:def 9;
  hence thesis by A2,A9,A8,A13,A12,A11,A10,A21,A20,A19,A18,A17,A16,A15,A14,A6
,A5,A4,A3,A7,ZFMISC_1:def 9;
end;
