Description: Inference from Theorem 19.21 of Margaris p. 90. (Restricted quantifier version.) For a version based on fewer axioms see ralrimdv . (Contributed by NM, 16-Feb-2004)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ralrimd.1 | |- F/ x ph |
|
ralrimd.2 | |- F/ x ps |
||
ralrimd.3 | |- ( ph -> ( ps -> ( x e. A -> ch ) ) ) |
||
Assertion | ralrimd | |- ( ph -> ( ps -> A. x e. A ch ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ralrimd.1 | |- F/ x ph |
|
2 | ralrimd.2 | |- F/ x ps |
|
3 | ralrimd.3 | |- ( ph -> ( ps -> ( x e. A -> ch ) ) ) |
|
4 | 1 2 3 | alrimd | |- ( ph -> ( ps -> A. x ( x e. A -> ch ) ) ) |
5 | df-ral | |- ( A. x e. A ch <-> A. x ( x e. A -> ch ) ) |
|
6 | 4 5 | imbitrrdi | |- ( ph -> ( ps -> A. x e. A ch ) ) |