defpred S₁[ object ] means $1 is strict MSSubAlgebra of U0;
for X1, X2 being set st ( for x being object holds
( x in X1 iff S₁[x] ) ) & ( for x being object holds
( x in X2 iff S₁[x] ) ) holds
X1 = X2 from XBOOLE_0:sch 3();
hence for b₁, b₂ being set st ( for x being object holds
( x in b₁ iff x is strict MSSubAlgebra of U0 ) ) & ( for x being object holds
( x in b₂ iff x is strict MSSubAlgebra of U0 ) ) holds
b₁ = b₂ ; :: thesis: verum