
theorem LM910:
  for A, B be Element of Class EqBL2Nat
  holds A+B = B+A
  proof
    let A, B be Element of Class EqBL2Nat;
    P0: A in Class EqBL2Nat & B in Class EqBL2Nat;
    consider x being object such that
    Q1: x in BOOLEAN* & A = Class (EqBL2Nat,x) by P0,EQREL_1:def 3;
    consider y being object such that
    Q2: y in BOOLEAN* & B = Class (EqBL2Nat,y) by P0,EQREL_1:def 3;
    reconsider x,y as Element of BOOLEAN* by Q1,Q2;
    R0: x in A & y in B by Q1,Q2,EQREL_1:20; then
    R1: A+B = Class (EqBL2Nat,x+y ) by LM800;
    L1: B+A = Class (EqBL2Nat,y+x ) by LM800,R0;
    QuBL2Nat.(A+B) = BL2Nat.(x+y) by LM700,R1
    .=BL2Nat.x+BL2Nat.y by LM240
    .= BL2Nat.(y+x) by LM240
    .= QuBL2Nat.(B+A) by L1,LM700;
    hence thesis by FUNCT_2:19;
  end;
