Description: Change bound variable. Uses only Tarski's FOL axiom schemes. See cbveu for a version with fewer disjoint variable conditions but requiring more axioms. (Contributed by NM, 25-Nov-1994) (Revised by Gino Giotto, 30-Sep-2024)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | cbveuvw.1 | |- ( x = y -> ( ph <-> ps ) ) |
|
| Assertion | cbveuvw | |- ( E! x ph <-> E! y ps ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cbveuvw.1 | |- ( x = y -> ( ph <-> ps ) ) |
|
| 2 | 1 | cbvexvw | |- ( E. x ph <-> E. y ps ) |
| 3 | 1 | cbvmovw | |- ( E* x ph <-> E* y ps ) |
| 4 | 2 3 | anbi12i | |- ( ( E. x ph /\ E* x ph ) <-> ( E. y ps /\ E* y ps ) ) |
| 5 | df-eu | |- ( E! x ph <-> ( E. x ph /\ E* x ph ) ) |
|
| 6 | df-eu | |- ( E! y ps <-> ( E. y ps /\ E* y ps ) ) |
|
| 7 | 4 5 6 | 3bitr4i | |- ( E! x ph <-> E! y ps ) |