let b1, b2 be BinOp of (UAAut UA); ( ( for x, y being Element of UAAut UA holds b1 . (x,y) = y * x ) & ( for x, y being Element of UAAut UA holds b2 . (x,y) = y * x ) implies b1 = b2 )
assume that
A2:
for x, y being Element of UAAut UA holds b1 . (x,y) = y * x
and
A3:
for x, y being Element of UAAut UA holds b2 . (x,y) = y * x
; b1 = b2
for x, y being Element of UAAut UA holds b1 . (x,y) = b2 . (x,y)
hence
b1 = b2
by BINOP_1:2; verum