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