let X1, X2 be Subset of Q; :: thesis: ( ( for x being Element of Q holds
( x in X1 iff for y being Element of Q holds x * y = y * x ) ) & ( for x being Element of Q holds
( x in X2 iff for y being Element of Q holds x * y = y * x ) ) implies X1 = X2 )
assume that
A9: for x being Element of Q holds
( x in X1 iff S₄[x] ) and
A10: for x being Element of Q holds
( x in X2 iff S₄[x] ) ; :: thesis: X1 = X2
thus X1 = X2 from SUBSET_1:sch 2(A9, A10); :: thesis: verum