Description: Implicit substitution of a class for a setvar variable. See also vtoclALT . (Contributed by NM, 30-Aug-1993) Remove dependency on ax-10 . (Revised by BJ, 29-Nov-2020) (Proof shortened by SN, 20-Apr-2024)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | vtocl.1 | |- A e. _V |
|
| vtocl.2 | |- ( x = A -> ( ph <-> ps ) ) |
||
| vtocl.3 | |- ph |
||
| Assertion | vtocl | |- ps |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | vtocl.1 | |- A e. _V |
|
| 2 | vtocl.2 | |- ( x = A -> ( ph <-> ps ) ) |
|
| 3 | vtocl.3 | |- ph |
|
| 4 | 3 2 | mpbii | |- ( x = A -> ps ) |
| 5 | 1 | isseti | |- E. x x = A |
| 6 | 4 5 | exlimiiv | |- ps |