<s>
As	O
a	O
demonstration	O
of	O
the	O
principle	O
,	O
consider	O
two	O
contradictory	O
statements	O
—	O
"	O
All	O
lemons	B-Application
are	O
yellow	O
"	O
and	O
"	O
Not	O
all	O
lemons	B-Application
are	O
yellow	O
"	O
—	O
and	O
suppose	O
that	O
both	O
are	O
true	O
.	O
</s>
<s>
If	O
that	O
is	O
the	O
case	O
,	O
anything	O
can	O
be	O
proven	O
,	O
e.g.	O
,	O
the	O
assertion	O
that	O
"	O
unicorns	B-Application
exist	O
"	O
,	O
by	O
using	O
the	O
following	O
argument	O
:	O
</s>
<s>
We	O
know	O
that	O
"	O
Not	O
all	O
lemons	B-Application
are	O
yellow	O
"	O
,	O
as	O
it	O
has	O
been	O
assumed	O
to	O
be	O
true	O
.	O
</s>
<s>
We	O
know	O
that	O
"	O
All	O
lemons	B-Application
are	O
yellow	O
"	O
,	O
as	O
it	O
has	O
been	O
assumed	O
to	O
be	O
true	O
.	O
</s>
<s>
Therefore	O
,	O
the	O
two-part	O
statement	O
"	O
All	O
lemons	B-Application
are	O
yellow	O
or	O
unicorns	B-Application
exist	O
"	O
must	O
also	O
be	O
true	O
,	O
since	O
the	O
first	O
part	O
"	O
All	O
lemons	B-Application
are	O
yellow	O
"	O
of	O
the	O
two-part	O
statement	O
is	O
true	O
(	O
as	O
this	O
has	O
been	O
assumed	O
)	O
.	O
</s>
<s>
However	O
,	O
since	O
we	O
know	O
that	O
"	O
Not	O
all	O
lemons	B-Application
are	O
yellow	O
"	O
(	O
as	O
this	O
has	O
been	O
assumed	O
)	O
,	O
the	O
first	O
part	O
is	O
false	O
,	O
and	O
hence	O
the	O
second	O
part	O
must	O
be	O
true	O
to	O
ensure	O
the	O
two-part	O
statement	O
to	O
be	O
true	O
,	O
i.e.	O
,	O
unicorns	B-Application
exist	O
.	O
</s>
<s>
This	O
is	O
just	O
the	O
symbolic	O
version	O
of	O
the	O
informal	O
argument	O
given	O
in	O
the	O
introduction	O
,	O
with	O
standing	O
for	O
"	O
all	O
lemons	B-Application
are	O
yellow	O
"	O
and	O
standing	O
for	O
"	O
Unicorns	B-Application
exist	O
"	O
.	O
</s>
<s>
We	O
start	O
out	O
by	O
assuming	O
that	O
(	O
1	O
)	O
all	O
lemons	B-Application
are	O
yellow	O
and	O
that	O
(	O
2	O
)	O
not	O
all	O
lemons	B-Application
are	O
yellow	O
.	O
</s>
<s>
From	O
the	O
proposition	O
that	O
all	O
lemons	B-Application
are	O
yellow	O
,	O
we	O
infer	O
that	O
(	O
3	O
)	O
either	O
all	O
lemons	B-Application
are	O
yellow	O
or	O
unicorns	B-Application
exist	O
.	O
</s>
<s>
But	O
then	O
from	O
this	O
and	O
the	O
fact	O
that	O
not	O
all	O
lemons	B-Application
are	O
yellow	O
,	O
we	O
infer	O
that	O
(	O
4	O
)	O
unicorns	B-Application
exist	O
by	O
disjunctive	O
syllogism	O
.	O
</s>
<s>
Reduction	O
in	O
proof	O
strength	O
of	O
logics	O
without	O
ex	B-Error_Name
falso	I-Error_Name
are	O
discussed	O
in	O
minimal	O
logic	O
.	O
</s>
