let X1, X2 be Element of F₁(); :: thesis: ( ( for x being object holds
( x in X1 iff P₁[x] ) ) & ( for x being object holds
( x in X2 iff P₁[x] ) ) implies X1 = X2 )
assume that
A1: for x being object holds
( x in X1 iff P₁[x] ) and
A2: for x being object holds
( x in X2 iff P₁[x] ) ; :: thesis: X1 = X2
for x being object holds
( x in X1 iff x in X2 ) by A1, A2;
hence X1 = X2 by TARSKI:2; :: thesis: verum