Suspension of contractible space is contractible

Statement
Suppose $$X$$ is a uses property satisfaction of::contractible space. Then, the fact about::suspension of $$X$$, denoted $$SX$$, is also a proves property satisfaction of::contractible space.

Related facts

 * Suspension of any space is path-connected
 * Suspension of path-connected space is simply connected, which uses the Seifert-van Kampen theorem
 * Homology for suspension, which uses the Mayer-Vietoris homology sequence
 * Suspension pushes up connectivity by one
 * Suspension of weakly contractible space is weakly contractible