Description: Formula-building lemma for use with the Distinctor Reduction Theorem. Version of drex1 with a disjoint variable condition, which does not require ax-13 . (Contributed by NM, 27-Feb-2005) (Revised by BJ, 17-Jun-2019)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | dral1v.1 | |- ( A. x x = y -> ( ph <-> ps ) ) |
|
| Assertion | drex1v | |- ( A. x x = y -> ( E. x ph <-> E. y ps ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | dral1v.1 | |- ( A. x x = y -> ( ph <-> ps ) ) |
|
| 2 | 1 | notbid | |- ( A. x x = y -> ( -. ph <-> -. ps ) ) |
| 3 | 2 | dral1v | |- ( A. x x = y -> ( A. x -. ph <-> A. y -. ps ) ) |
| 4 | 3 | notbid | |- ( A. x x = y -> ( -. A. x -. ph <-> -. A. y -. ps ) ) |
| 5 | df-ex | |- ( E. x ph <-> -. A. x -. ph ) |
|
| 6 | df-ex | |- ( E. y ps <-> -. A. y -. ps ) |
|
| 7 | 4 5 6 | 3bitr4g | |- ( A. x x = y -> ( E. x ph <-> E. y ps ) ) |