let A1, A2 be a_partition of Y; :: thesis: ( ( for d being set holds
( d in A1 iff d is_min_depend PA,PB ) ) & ( for d being set holds
( d in A2 iff d is_min_depend PA,PB ) ) implies A1 = A2 )
assume that
A26: for x being set holds
( x in A1 iff x is_min_depend PA,PB ) and
A27: for x being set holds
( x in A2 iff x is_min_depend PA,PB ) ; :: thesis: A1 = A2
for y being object holds
( y in A1 iff y in A2 ) by A26, A27;
hence A1 = A2 by TARSKI:2; :: thesis: verum