let P, Q be PLANE of S; :: thesis: ( K on P & L on P & K on Q & L on Q implies P = Q ) assume A3:
( K on P & L on P & K on Q & L on Q )
; :: thesis: P = Q consider P1 being PLANE of S such that A4:
for P2 being PLANE of S holds ( ( K on P2 & L on P2 ) iff P1 = P2 )
by A1, A2, Th49;
( P = P1 & Q = P1 )
by A3, A4; hence
P = Q
; :: thesis: verum