Description: Restricted quantifier version of 19.29 . See also r19.29r . (Contributed by NM, 31-Aug-1999) (Proof shortened by Andrew Salmon, 30-May-2011) (Proof shortened by Wolf Lammen, 22-Dec-2024)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | r19.29 | |- ( ( A. x e. A ph /\ E. x e. A ps ) -> E. x e. A ( ph /\ ps ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ibar | |- ( ph -> ( ps <-> ( ph /\ ps ) ) ) |
|
| 2 | 1 | ralrexbid | |- ( A. x e. A ph -> ( E. x e. A ps <-> E. x e. A ( ph /\ ps ) ) ) |
| 3 | 2 | biimpa | |- ( ( A. x e. A ph /\ E. x e. A ps ) -> E. x e. A ( ph /\ ps ) ) |