let p, q, r, s be Point of TarskiEuclid2Space; ( between p,q,r & between p,r,s implies between p,q,s )
assume that
A1:
between p,q,r
and
A2:
between p,r,s
; between p,q,s
( Tn2TR q in LSeg ((Tn2TR p),(Tn2TR r)) & Tn2TR r in LSeg ((Tn2TR p),(Tn2TR s)) )
by A1, A2, ThConv6;
hence
between p,q,s
by ThConv6, THORANGE; verum