
theorem LM700:
  for x be Element of BOOLEAN*
  holds QuBL2Nat.(Class (EqBL2Nat,x)) =BL2Nat.x
  proof
    let x be Element of BOOLEAN*;
    reconsider A = Class (EqBL2Nat,x)
    as Element of Class EqBL2Nat by EQREL_1:def 3;
    reconsider A0 = A as Subset of BOOLEAN*;
    consider x1 being object such that
    P1: x1 in A0 & QuBL2Nat.A0 =BL2Nat.x1 by Def400;
    reconsider x1 as Element of BOOLEAN* by P1;
    Class (EqBL2Nat,x1) = Class (EqBL2Nat,x) by P1,EQREL_1:23;
    then
    [x1,x] in EqBL2Nat by EQREL_1:35;
    hence thesis by P1,Def300;
  end;
