Consider the initial value problem for a first-order differential equation
\[
y
′
=
f
(
x
,
y
)
,
y
(
x
0
)
=
y
0
.
y’ = f(x,y),\quad y({x_0}) = {y_0}.
\]
In this paper a new uniqueness criterion is proved. This criterion is related to the numeric equation
\[
u
=
y
0
+
(
t
−
x
0
)
f
(
t
,
u
)
.
u = {y_0} + (t - {x_0})f(t,u).
\]
It is also shown that some well-known uniqueness theorems are consequences of our result.