theorem
  M,v |= p 'or' q => q 'or' p & M |= p 'or' q => q 'or' p
proof
  now
    let v;
A1: M,v |= p or M,v |= q implies M,v |= q 'or' p by ZF_MODEL:17;
    M,v |= p 'or' q implies M,v |= p or M,v |= q by ZF_MODEL:17;
    hence M,v |= p 'or' q => q 'or' p by A1,ZF_MODEL:18;
  end;
  hence thesis;
end;
