Description: A member of an unordered triple of classes is one of them. Special case of Exercise 1 of TakeutiZaring p. 17. (Contributed by NM, 8-Apr-1994) (Revised by Mario Carneiro, 11-Feb-2015)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | eltp.1 | |- A e. _V |
|
| Assertion | eltp | |- ( A e. { B , C , D } <-> ( A = B \/ A = C \/ A = D ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | eltp.1 | |- A e. _V |
|
| 2 | eltpg | |- ( A e. _V -> ( A e. { B , C , D } <-> ( A = B \/ A = C \/ A = D ) ) ) |
|
| 3 | 1 2 | ax-mp | |- ( A e. { B , C , D } <-> ( A = B \/ A = C \/ A = D ) ) |