Description: Rule used to change the bound variable in an existential quantifier with implicit substitution. Deduction form. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker cbvexdvaw if possible. (Contributed by David Moews, 1-May-2017) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | cbvaldva.1 | |- ( ( ph /\ x = y ) -> ( ps <-> ch ) ) |
|
| Assertion | cbvexdva | |- ( ph -> ( E. x ps <-> E. y ch ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cbvaldva.1 | |- ( ( ph /\ x = y ) -> ( ps <-> ch ) ) |
|
| 2 | nfv | |- F/ y ph |
|
| 3 | nfvd | |- ( ph -> F/ y ps ) |
|
| 4 | 1 | ex | |- ( ph -> ( x = y -> ( ps <-> ch ) ) ) |
| 5 | 2 3 4 | cbvexd | |- ( ph -> ( E. x ps <-> E. y ch ) ) |