let PS be ParSp; for a, b, c, d being Element of PS st a,b '||' c,d holds
c,d '||' a,b
let a, b, c, d be Element of PS; ( a,b '||' c,d implies c,d '||' a,b )
assume A1:
a,b '||' c,d
; c,d '||' a,b
a,b '||' a,b
by Th18;
then
( a <> b implies c,d '||' a,b )
by A1, Def11;
hence
c,d '||' a,b
by Def11; verum