defpred S₁[ object ] means $1 is finite Tree;
let T1, T2 be Subset of Trees; :: thesis: ( ( for x being object holds
( x in T1 iff x is finite Tree ) ) & ( for x being object holds
( x in T2 iff x is finite Tree ) ) implies T1 = T2 )
assume that
A1: for x being object holds
( x in T1 iff S₁[x] ) and
A2: for x being object holds
( x in T2 iff S₁[x] ) ; :: thesis: T1 = T2
thus T1 = T2 from XBOOLE_0:sch 2(A1, A2); :: thesis: verum