let
L
be non
empty
satisfying_Sh_1
ShefferStr
;
:: thesis:
for
x
,
y
,
z
being
Element
of
L
holds
(
x

y
)

z
=
z

(
y

x
)
let
x
,
y
,
z
be
Element
of
L
;
:: thesis:
(
x

y
)

z
=
z

(
y

x
)
set
X
=
x

y
;
(
x

y
)

z
=
z

(
x

y
)
by
Th20
;
hence
(
x

y
)

z
=
z

(
y

x
)
by
Th33
;
:: thesis:
verum