let o, p, q, r be Point of (TOP-REAL 3); ( |{o,p,((o <X> p) <X> (q <X> r))}| = 0 & |{q,r,((o <X> p) <X> (q <X> r))}| = 0 )
set s = (o <X> p) <X> (q <X> r);
thus |{o,p,((o <X> p) <X> (q <X> r))}| =
|((o <X> p),((o <X> p) <X> (q <X> r)))|
by EUCLID_5:35
.=
0
by Th38
; |{q,r,((o <X> p) <X> (q <X> r))}| = 0
thus |{q,r,((o <X> p) <X> (q <X> r))}| =
|((q <X> r),((o <X> p) <X> (q <X> r)))|
by EUCLID_5:35
.=
0
by Th39
; verum