Description: A transitive class is equal to the union of its successor, inference form. Combines Theorem 4E of Enderton p. 72 and Exercise 6 of Enderton p. 73. (Contributed by NM, 30-Aug-1993)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | unisuc.1 | |- A e. _V |
|
| Assertion | unisuc | |- ( Tr A <-> U. suc A = A ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | unisuc.1 | |- A e. _V |
|
| 2 | unisucg | |- ( A e. _V -> ( Tr A <-> U. suc A = A ) ) |
|
| 3 | 1 2 | ax-mp | |- ( Tr A <-> U. suc A = A ) |