Description: Formula-building rule for restricted existential quantifier (inference form). (Contributed by NM, 14-Nov-2004)
Ref | Expression | ||
---|---|---|---|
Hypothesis | reubiia.1 | |- ( x e. A -> ( ph <-> ps ) ) |
|
Assertion | reubiia | |- ( E! x e. A ph <-> E! x e. A ps ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | reubiia.1 | |- ( x e. A -> ( ph <-> ps ) ) |
|
2 | 1 | pm5.32i | |- ( ( x e. A /\ ph ) <-> ( x e. A /\ ps ) ) |
3 | 2 | eubii | |- ( E! x ( x e. A /\ ph ) <-> E! x ( x e. A /\ ps ) ) |
4 | df-reu | |- ( E! x e. A ph <-> E! x ( x e. A /\ ph ) ) |
|
5 | df-reu | |- ( E! x e. A ps <-> E! x ( x e. A /\ ps ) ) |
|
6 | 3 4 5 | 3bitr4i | |- ( E! x e. A ph <-> E! x e. A ps ) |