Description: The empty relation is hereditary in any class. (Contributed by RP, 27-Mar-2020) (New usage is discouraged.) (Proof modification is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | 0heALT | |- (/) hereditary A |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | xphe | |- ( (/) X. A ) hereditary A |
|
| 2 | 0xp | |- ( (/) X. A ) = (/) |
|
| 3 | heeq1 | |- ( ( (/) X. A ) = (/) -> ( ( (/) X. A ) hereditary A <-> (/) hereditary A ) ) |
|
| 4 | 2 3 | ax-mp | |- ( ( (/) X. A ) hereditary A <-> (/) hereditary A ) |
| 5 | 1 4 | mpbi | |- (/) hereditary A |