let IPP be Fanoian IncProjSp; :: thesis: ex p, q, r, s, a, b, c being POINT of IPP ex A, B, C, Q, L, R, S, D being LINE of IPP st
( not q on L & not r on L & not p on Q & not s on Q & not p on R & not r on R & not q on S & not s on S & {a,p,s} on L & {a,q,r} on Q & {b,q,s} on R & {b,p,r} on S & {c,p,q} on A & {c,r,s} on B & {a,b} on C & not c on C )
ex p, q, r, s, a, b, c being POINT of IPP ex A, B, C, Q, L, R, S, D being LINE of IPP ex d being POINT of IPP st
( not q on L & not r on L & not p on Q & not s on Q & not p on R & not r on R & not q on S & not s on S & {a,p,s} on L & {a,q,r} on Q & {b,q,s} on R & {b,p,r} on S & {c,p,q} on A & {c,r,s} on B & {a,b} on C & not c on C & b on D & c on D & C,D,R,S are_mutually_distinct & d on A & c,d,p,q are_mutually_distinct ) by Lm2;
hence ex p, q, r, s, a, b, c being POINT of IPP ex A, B, C, Q, L, R, S, D being LINE of IPP st
( not q on L & not r on L & not p on Q & not s on Q & not p on R & not r on R & not q on S & not s on S & {a,p,s} on L & {a,q,r} on Q & {b,q,s} on R & {b,p,r} on S & {c,p,q} on A & {c,r,s} on B & {a,b} on C & not c on C ) ; :: thesis: verum