let A1, A2 be Subset of L; :: thesis: ( ( for x being Element of L holds
( x in A1 iff x is atom ) ) & ( for x being Element of L holds
( x in A2 iff x is atom ) ) implies A1 = A2 )
assume that
A2: for x being Element of L holds
( x in A1 iff x is atom ) and
A3: for x being Element of L holds
( x in A2 iff x is atom ) ; :: thesis: A1 = A2
for x being object holds
( x in A1 iff x in A2 ) by A2, A3;
hence A1 = A2 by TARSKI:2; :: thesis: verum