let P, Q be PLANE of S; :: thesis: ( A on P & L on P & A on Q & L on Q implies P = Q )
assume A2: ( A on P & L on P & A on Q & L on Q ) ; :: thesis: P = Q
consider P1 being PLANE of S such that
A3: for P2 being PLANE of S holds
( ( A on P2 & L on P2 ) iff P1 = P2 ) by A1, Th48;
( P1 = P & P1 = Q ) by A2, A3;
hence P = Q ; :: thesis: verum