In Diamond-Shurman A first course in Modular forms p.334 Prop. 8.4.4. It is stated,
For E elliptic curve over $\bar{\mathbb{Q}}$ with good reduction at the prime ideal $\mathfrak{p}$ the reduction map on the N-torsion, $$E[N] \rightarrow \tilde{E}[N]$$ is surjective for all N.
The authors then state that this is beyond the scope of the book and give no reference. My searches have been unfruitful and I was wondering if there was a location where this proof could be found.
See. The Arithmetic of Elliptic Curves, J.H. Silverman, Springer. Perhaps in future be more patient before cross-posting!
Regards,
Central Ramifistation.
https://mathoverflow.net/questions/195105/proof-of-a-proposition-regarding-the-reduction-of-n-torsion-groups-on-elliptic-c