Description: One of the two elements in an ordered pair. (Contributed by NM, 15-Jul-1993) (Revised by Mario Carneiro, 26-Apr-2015) (Avoid depending on this detail.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | opi1.1 | |- A e. _V |
|
| opi1.2 | |- B e. _V |
||
| Assertion | opi1 | |- { A } e. <. A , B >. |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | opi1.1 | |- A e. _V |
|
| 2 | opi1.2 | |- B e. _V |
|
| 3 | snex | |- { A } e. _V |
|
| 4 | 3 | prid1 | |- { A } e. { { A } , { A , B } } |
| 5 | 1 2 | dfop | |- <. A , B >. = { { A } , { A , B } } |
| 6 | 4 5 | eleqtrri | |- { A } e. <. A , B >. |