let X1, X2 be Subset of AS; :: thesis: ( ( for x being Element of AS holds
( x in X1 iff LIN a,b,x ) ) & ( for x being Element of AS holds
( x in X2 iff LIN a,b,x ) ) implies X1 = X2 )
assume that
A2: for x being Element of AS holds
( x in X1 iff LIN a,b,x ) and
A3: for x being Element of AS holds
( x in X2 iff LIN a,b,x ) ; :: thesis: X1 = X2
for x being object holds
( x in X1 iff x in X2 ) by A2, A3;
hence X1 = X2 by TARSKI:2; :: thesis: verum