defpred S_{1}[ object ] means $1 is strict MSSubAlgebra of U0;

for X1, X2 being set st ( for x being object holds

( x in X1 iff S_{1}[x] ) ) & ( for x being object holds

( x in X2 iff S_{1}[x] ) ) holds

X1 = X2 from XBOOLE_0:sch 3();

hence for b_{1}, b_{2} being set st ( for x being object holds

( x in b_{1} iff x is strict MSSubAlgebra of U0 ) ) & ( for x being object holds

( x in b_{2} iff x is strict MSSubAlgebra of U0 ) ) holds

b_{1} = b_{2}
; :: thesis: verum

for X1, X2 being set st ( for x being object holds

( x in X1 iff S

( x in X2 iff S

X1 = X2 from XBOOLE_0:sch 3();

hence for b

( x in b

( x in b

b