Description: Deduction quantifying both antecedent and consequent, based on Theorem 19.22 of Margaris p. 90. (Contributed by NM, 14-Nov-2002) Reduce dependencies on axioms. (Revised by Wolf Lammen, 8-Jan-2020)
Ref | Expression | ||
---|---|---|---|
Hypothesis | reximdvai.1 | |- ( ph -> ( x e. A -> ( ps -> ch ) ) ) |
|
Assertion | reximdvai | |- ( ph -> ( E. x e. A ps -> E. x e. A ch ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | reximdvai.1 | |- ( ph -> ( x e. A -> ( ps -> ch ) ) ) |
|
2 | 1 | ralrimiv | |- ( ph -> A. x e. A ( ps -> ch ) ) |
3 | rexim | |- ( A. x e. A ( ps -> ch ) -> ( E. x e. A ps -> E. x e. A ch ) ) |
|
4 | 2 3 | syl | |- ( ph -> ( E. x e. A ps -> E. x e. A ch ) ) |