defpred S₁[ set ] means $1 is strict Subgraph of G;
let X1, X2 be set ; :: thesis: ( ( for x being set holds
( x in X1 iff x is strict Subgraph of G ) ) & ( for x being set holds
( x in X2 iff x is strict Subgraph of G ) ) implies X1 = X2 )
assume that
A12: for x being set holds
( x in X1 iff S₁[x] ) and
A13: for x being set holds
( x in X2 iff S₁[x] ) ; :: thesis: X1 = X2
thus X1 = X2 from XBOOLE_0:sch 2(A12, A13); :: thesis: verum