Description: Inference from equality of a class variable and a restricted class abstraction. (Contributed by NM, 16-Feb-2004)
Ref | Expression | ||
---|---|---|---|
Hypothesis | rabeq2i.1 | |- A = { x e. B | ph } |
|
Assertion | rabeq2i | |- ( x e. A <-> ( x e. B /\ ph ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rabeq2i.1 | |- A = { x e. B | ph } |
|
2 | 1 | eleq2i | |- ( x e. A <-> x e. { x e. B | ph } ) |
3 | rabid | |- ( x e. { x e. B | ph } <-> ( x e. B /\ ph ) ) |
|
4 | 2 3 | bitri | |- ( x e. A <-> ( x e. B /\ ph ) ) |