let it1, it2 be Subset of G; ( ( for e being set holds
( e in it1 iff ( e in G & card e = 2 ) ) ) & ( for e being set holds
( e in it2 iff ( e in G & card e = 2 ) ) ) implies it1 = it2 )
assume that
A2:
for e being set holds
( e in it1 iff ( e in G & card e = 2 ) )
and
A3:
for e being set holds
( e in it2 iff ( e in G & card e = 2 ) )
; it1 = it2
hence
it1 = it2
by TARSKI:2; verum