Description: Inference from Theorem 19.21 of Margaris p. 90 (restricted quantifier version). (Contributed by Glauco Siliprandi, 23-Oct-2021)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ralrimia.1 | |- F/ x ph |
|
ralrimia.2 | |- ( ( ph /\ x e. A ) -> ps ) |
||
Assertion | ralrimia | |- ( ph -> A. x e. A ps ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ralrimia.1 | |- F/ x ph |
|
2 | ralrimia.2 | |- ( ( ph /\ x e. A ) -> ps ) |
|
3 | 2 | ex | |- ( ph -> ( x e. A -> ps ) ) |
4 | 1 3 | ralrimi | |- ( ph -> A. x e. A ps ) |