defpred S₁[ set ] means ex a, b, c, d being Element of [: the carrier of F, the carrier of F, the carrier of F:] st
( $1 = [a,b,c,d] & (((a `1) - (b `1)) * ((c `2) - (d `2))) - (((c `1) - (d `1)) * ((a `2) - (b `2))) = 0. F & (((a `1) - (b `1)) * ((c `3) - (d `3))) - (((c `1) - (d `1)) * ((a `3) - (b `3))) = 0. F & (((a `2) - (b `2)) * ((c `3) - (d `3))) - (((c `2) - (d `2)) * ((a `3) - (b `3))) = 0. F );
thus ex X being set st
for x being set holds
( x in X iff ( x in 4C3 F & S₁[x] ) ) from XBOOLE_0:sch 1(); :: thesis: verum