Description: Obsolete version of rabeqc as of 15-Jan-2025. (Contributed by AV, 20-Apr-2022) (Proof modification is discouraged.) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypothesis | rabeqcOLD.1 | |- ( x e. A -> ph ) |
|
Assertion | rabeqcOLD | |- { x e. A | ph } = A |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rabeqcOLD.1 | |- ( x e. A -> ph ) |
|
2 | df-rab | |- { x e. A | ph } = { x | ( x e. A /\ ph ) } |
|
3 | eqabcb | |- ( { x | ( x e. A /\ ph ) } = A <-> A. x ( ( x e. A /\ ph ) <-> x e. A ) ) |
|
4 | 1 | pm4.71i | |- ( x e. A <-> ( x e. A /\ ph ) ) |
5 | 4 | bicomi | |- ( ( x e. A /\ ph ) <-> x e. A ) |
6 | 3 5 | mpgbir | |- { x | ( x e. A /\ ph ) } = A |
7 | 2 6 | eqtri | |- { x e. A | ph } = A |