Description: Obsolete version of brdomi as of 29-Nov-2024. (Contributed by Mario Carneiro, 26-Apr-2015) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | brdomiOLD | |- ( A ~<_ B -> E. f f : A -1-1-> B ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | reldom | |- Rel ~<_ |
|
| 2 | 1 | brrelex2i | |- ( A ~<_ B -> B e. _V ) |
| 3 | brdomg | |- ( B e. _V -> ( A ~<_ B <-> E. f f : A -1-1-> B ) ) |
|
| 4 | 2 3 | syl | |- ( A ~<_ B -> ( A ~<_ B <-> E. f f : A -1-1-> B ) ) |
| 5 | 4 | ibi | |- ( A ~<_ B -> E. f f : A -1-1-> B ) |