Full Idea
Since non-Euclidean geometry preserves all Euclid's postulates except the fifth one, all the theorems derived without the use of the fifth postulate remain valid.
Gist of Idea
In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate
Source
Michal Walicki (Introduction to Mathematical Logic [2012], 4.1)
Book Reference
Walicki,Michal: 'Introduction to Mathematical Logic' [World Scientific 2012], p.122