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

A2: now

assume a = b ; :: thesis: b,a congr d,c
then ( a = b & c = d ) by A1, Th55;
hence b,a congr d,c by Def4; :: thesis: verum

end;

now

assume a <> b ; :: thesis: b,a congr d,c
then consider p, q being Element of FdSp such that
A3: ( parallelogram p,q,a,b & parallelogram p,q,c,d ) by A1, Def4;
( parallelogram q,p,b,a & parallelogram q,p,d,c ) by A3, Th41;
hence b,a congr d,c by Def4; :: thesis: verum

end;

hence b,a congr d,c by A2; :: thesis: verum