let SAS be Semi_Affine_Space; :: thesis: for a, b, c, d being Element of SAS st congr a,b,c,d holds
a,b // c,d
let a, b, c, d be Element of SAS; :: thesis: ( congr a,b,c,d implies a,b // c,d )
assume A1: congr a,b,c,d ; :: thesis: a,b // c,d

now

assume a <> b ; :: thesis: a,b // c,d
then consider p, q being Element of SAS such that
A2: ( parallelogram p,q,a,b & parallelogram p,q,c,d ) by A1, Def4;
( p <> q & p,q // a,b & p,q // c,d ) by A2, Def3, Th54;
hence a,b // c,d by Def1; :: thesis: verum

end;

hence a,b // c,d by Th14; :: thesis: verum