Description: Version of rabbidva2 with disjoint variable condition replaced by nonfreeness hypothesis. (Contributed by BJ, 27-Apr-2019)
Ref | Expression | ||
---|---|---|---|
Hypotheses | bj-rabbida2.nf | |- F/ x ph |
|
bj-rabbida2.1 | |- ( ph -> ( ( x e. A /\ ps ) <-> ( x e. B /\ ch ) ) ) |
||
Assertion | bj-rabbida2 | |- ( ph -> { x e. A | ps } = { x e. B | ch } ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-rabbida2.nf | |- F/ x ph |
|
2 | bj-rabbida2.1 | |- ( ph -> ( ( x e. A /\ ps ) <-> ( x e. B /\ ch ) ) ) |
|
3 | 1 2 | abbid | |- ( ph -> { x | ( x e. A /\ ps ) } = { x | ( x e. B /\ ch ) } ) |
4 | df-rab | |- { x e. A | ps } = { x | ( x e. A /\ ps ) } |
|
5 | df-rab | |- { x e. B | ch } = { x | ( x e. B /\ ch ) } |
|
6 | 3 4 5 | 3eqtr4g | |- ( ph -> { x e. A | ps } = { x e. B | ch } ) |