let x, y be Element of REAL ; opp (+ x,y) = + (opp x),(opp y)
+ (+ x,y),(+ (opp x),(opp y)) =
+ x,(+ y,(+ (opp x),(opp y)))
by Th25
.=
+ x,(+ (opp x),(+ y,(opp y)))
by Th25
.=
+ x,(+ (opp x),o)
by Def4
.=
+ x,(opp x)
by Th13
.=
0
by Def4
;
hence
opp (+ x,y) = + (opp x),(opp y)
by Def4; verum