Description: If a class is not finite, then it contains at least one element. (Contributed by Alexander van der Vekens, 12-Jan-2018)
Ref | Expression | ||
---|---|---|---|
Assertion | nfielex | |- ( -. A e. Fin -> E. x x e. A ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0fin | |- (/) e. Fin |
|
2 | eleq1 | |- ( A = (/) -> ( A e. Fin <-> (/) e. Fin ) ) |
|
3 | 1 2 | mpbiri | |- ( A = (/) -> A e. Fin ) |
4 | 3 | con3i | |- ( -. A e. Fin -> -. A = (/) ) |
5 | neq0 | |- ( -. A = (/) <-> E. x x e. A ) |
|
6 | 4 5 | sylib | |- ( -. A e. Fin -> E. x x e. A ) |