Description: An infinite sequence of complex numbers converges to at most one limit. (Contributed by Mario Carneiro, 13-Jul-2013)
Ref | Expression | ||
---|---|---|---|
Assertion | climmo | |- E* x F ~~> x |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breq2 | |- ( x = y -> ( F ~~> x <-> F ~~> y ) ) |
|
2 | 1 | cbvexvw | |- ( E. x F ~~> x <-> E. y F ~~> y ) |
3 | climeu | |- ( F ~~> y -> E! x F ~~> x ) |
|
4 | 3 | exlimiv | |- ( E. y F ~~> y -> E! x F ~~> x ) |
5 | 2 4 | sylbi | |- ( E. x F ~~> x -> E! x F ~~> x ) |
6 | moeu | |- ( E* x F ~~> x <-> ( E. x F ~~> x -> E! x F ~~> x ) ) |
|
7 | 5 6 | mpbir | |- E* x F ~~> x |