Description: The intersection of the empty set is the universal class. Exercise 2 of TakeutiZaring p. 44. (Contributed by NM, 18-Aug-1993) (Proof shortened by JJ, 26-Jul-2021)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | int0 | |- |^| (/) = _V |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ral0 | |- A. x e. (/) y e. x |
|
| 2 | vex | |- y e. _V |
|
| 3 | 2 | elint2 | |- ( y e. |^| (/) <-> A. x e. (/) y e. x ) |
| 4 | 1 3 | mpbir | |- y e. |^| (/) |
| 5 | 4 2 | 2th | |- ( y e. |^| (/) <-> y e. _V ) |
| 6 | 5 | eqriv | |- |^| (/) = _V |