let n be Nat; :: thesis: for L1, L2 being Element of line_of_REAL n st L1 // L2 & L1 <> L2 holds
ex P being Element of plane_of_REAL n st
( L1 c= P & L2 c= P & P is being_plane )
let L1, L2 be Element of line_of_REAL n; :: thesis: ( L1 // L2 & L1 <> L2 implies ex P being Element of plane_of_REAL n st
( L1 c= P & L2 c= P & P is being_plane ) )
assume that
A1: L1 // L2 and
A2: L1 <> L2 ; :: thesis: ex P being Element of plane_of_REAL n st
( L1 c= P & L2 c= P & P is being_plane )
A3: L2 is being_line by A1, Th66;
( L1,L2 are_coplane & L1 is being_line ) by A1, Th66, Th97;
hence ex P being Element of plane_of_REAL n st
( L1 c= P & L2 c= P & P is being_plane ) by A1, A2, A3, Th71, Th98; :: thesis: verum