Description: The difference between a class and itself is the empty set. Proposition 5.15 of TakeutiZaring p. 20. Also Theorem 32 of Suppes p. 28. (Contributed by NM, 22-Apr-2004)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | difid | |- ( A \ A ) = (/) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ssid | |- A C_ A |
|
| 2 | ssdif0 | |- ( A C_ A <-> ( A \ A ) = (/) ) |
|
| 3 | 1 2 | mpbi | |- ( A \ A ) = (/) |