Assume Playfair and let lines "m" and "n" be parallel to line L. If "m" is NOT equal to "n", and "m" and "n" intersect at P, then we would have two different lines parallel to L through P, contradicting Playfair. Thus, either m and n are parallel, or are the same line.

Conversely, assume that two lines parallel to the same line are equal or themselves parallel. Let l be a line and suppose "m" and "n" are parallel to L at a point P not on L. Then, "m" and "n" must be equal, as they intersect at P.

Please make a drawing explaining this answer.

(Survey of Geometry)