Description: Obsolete version of ralprg as of 30-Sep-2024. (Contributed by NM, 17-Sep-2011) (Revised by Mario Carneiro, 23-Apr-2015) (Proof shortened by AV, 8-Apr-2023) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | ralprg.1 | |- ( x = A -> ( ph <-> ps ) ) |
|
| ralprg.2 | |- ( x = B -> ( ph <-> ch ) ) |
||
| Assertion | ralprgOLD | |- ( ( A e. V /\ B e. W ) -> ( A. x e. { A , B } ph <-> ( ps /\ ch ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ralprg.1 | |- ( x = A -> ( ph <-> ps ) ) |
|
| 2 | ralprg.2 | |- ( x = B -> ( ph <-> ch ) ) |
|
| 3 | nfv | |- F/ x ps |
|
| 4 | nfv | |- F/ x ch |
|
| 5 | 3 4 1 2 | ralprgf | |- ( ( A e. V /\ B e. W ) -> ( A. x e. { A , B } ph <-> ( ps /\ ch ) ) ) |