let P, Q be PLANE of S; ( K on P & L on P & K on Q & L on Q implies P = Q )
assume that
A3:
( K on P & L on P )
and
A4:
( K on Q & L on Q )
; P = Q
consider P1 being PLANE of S such that
A5:
for P2 being PLANE of S holds
( ( K on P2 & L on P2 ) iff P1 = P2 )
by A1, A2, Th27;
P = P1
by A3, A5;
hence
P = Q
by A4, A5; verum