Description: Inference from Theorem 19.21 of Margaris p. 90. (Restricted quantifier version.) (Contributed by NM, 27-May-1998) Reduce dependencies on axioms. (Revised by Wolf Lammen, 28-Dec-2019)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | ralrimdv.1 | |- ( ph -> ( ps -> ( x e. A -> ch ) ) ) |
|
| Assertion | ralrimdv | |- ( ph -> ( ps -> A. x e. A ch ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ralrimdv.1 | |- ( ph -> ( ps -> ( x e. A -> ch ) ) ) |
|
| 2 | 1 | imp | |- ( ( ph /\ ps ) -> ( x e. A -> ch ) ) |
| 3 | 2 | ralrimiv | |- ( ( ph /\ ps ) -> A. x e. A ch ) |
| 4 | 3 | ex | |- ( ph -> ( ps -> A. x e. A ch ) ) |