Description: Restricted quantifier version of 19.29r ; variation of r19.29 . (Contributed by NM, 31-Aug-1999) (Proof shortened by Wolf Lammen, 29-Jun-2023)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | r19.29r | |- ( ( E. x e. A ph /\ A. x e. A ps ) -> E. x e. A ( ph /\ ps ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | r19.29 | |- ( ( A. x e. A ps /\ E. x e. A ph ) -> E. x e. A ( ps /\ ph ) ) |
|
| 2 | 1 | ancoms | |- ( ( E. x e. A ph /\ A. x e. A ps ) -> E. x e. A ( ps /\ ph ) ) |
| 3 | pm3.22 | |- ( ( ps /\ ph ) -> ( ph /\ ps ) ) |
|
| 4 | 3 | reximi | |- ( E. x e. A ( ps /\ ph ) -> E. x e. A ( ph /\ ps ) ) |
| 5 | 2 4 | syl | |- ( ( E. x e. A ph /\ A. x e. A ps ) -> E. x e. A ( ph /\ ps ) ) |