Statement: Prove, under the assumption of the parallel postulate (P-1), parallelism of lines is transitive. That is if l||m and m||q, then l||q.
Parallel Postulate(p-1)-If l is any line and point P not on l there exists an unique line passing through P parallel to l( in the plane of P,l).
Proof- Assume to the contrary that l is not parallel to q. Further assume the parallel postulate p-1. Sine l is not parallel to q that means both lines meet at least 1 point.But that's a contradiction since it contradicts parallel postulate p-1.
Is that correct? or do i need to explain it a bit more why it contradicts?