let SAS be Semi_Affine_Space; for a, b, c, d being Element of SAS st congr a,b,c,d holds
( congr c,d,a,b & congr b,a,d,c & congr a,c,b,d & congr d,c,b,a & congr b,d,a,c & congr c,a,d,b & congr d,b,c,a )
let a, b, c, d be Element of SAS; ( congr a,b,c,d implies ( congr c,d,a,b & congr b,a,d,c & congr a,c,b,d & congr d,c,b,a & congr b,d,a,c & congr c,a,d,b & congr d,b,c,a ) )
assume A1:
congr a,b,c,d
; ( congr c,d,a,b & congr b,a,d,c & congr a,c,b,d & congr d,c,b,a & congr b,d,a,c & congr c,a,d,b & congr d,b,c,a )
then
congr c,d,a,b
;
then A2:
congr d,c,b,a
by Th67;
( congr b,a,d,c & congr a,c,b,d )
by A1, Th67, Th68;
hence
( congr c,d,a,b & congr b,a,d,c & congr a,c,b,d & congr d,c,b,a & congr b,d,a,c & congr c,a,d,b & congr d,b,c,a )
by A2, Th67, Th68; verum