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