Description: Uniqueness condition for the binary relation 1st . (Contributed by Scott Fenton, 11-Apr-2014) (Proof shortened by Mario Carneiro, 3-May-2015)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | br1steq.1 | |- A e. _V |
|
| br1steq.2 | |- B e. _V |
||
| Assertion | br1steq | |- ( <. A , B >. 1st C <-> C = A ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | br1steq.1 | |- A e. _V |
|
| 2 | br1steq.2 | |- B e. _V |
|
| 3 | br1steqg | |- ( ( A e. _V /\ B e. _V ) -> ( <. A , B >. 1st C <-> C = A ) ) |
|
| 4 | 1 2 3 | mp2an | |- ( <. A , B >. 1st C <-> C = A ) |