let n be Element of NAT ; :: thesis: for P1, P2 being Element of plane_of_REAL n st P1 is being_plane & P1 c= P2 holds
P1 = P2
let P1, P2 be Element of plane_of_REAL n; :: thesis: ( P1 is being_plane & P1 c= P2 implies P1 = P2 )
assume A1: ( P1 is being_plane & P1 c= P2 ) ; :: thesis: P1 = P2
then consider x1, x2, x3 being Element of REAL n such that
A2: ( x2 - x1,x3 - x1 are_lindependent2 & P1 = plane x1,x2,x3 ) by Def10;
( x1 in plane x1,x2,x3 & x2 in plane x1,x2,x3 & x3 in plane x1,x2,x3 ) by Th87;
hence P1 = P2 by A1, A2, Th97; :: thesis: verum