Description: Obsolete version of dral1v as of 18-Nov-2024. (Contributed by NM, 24-Nov-1994) (Revised by BJ, 17-Jun-2019) Base the proof on ax12v . (Revised by Wolf Lammen, 30-Mar-2024) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | dral1v.1 | |- ( A. x x = y -> ( ph <-> ps ) ) |
|
| Assertion | dral1vOLD | |- ( A. x x = y -> ( A. x ph <-> A. y ps ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | dral1v.1 | |- ( A. x x = y -> ( ph <-> ps ) ) |
|
| 2 | nfa1 | |- F/ x A. x x = y |
|
| 3 | 2 1 | albid | |- ( A. x x = y -> ( A. x ph <-> A. x ps ) ) |
| 4 | axc11v | |- ( A. x x = y -> ( A. x ps -> A. y ps ) ) |
|
| 5 | axc11rv | |- ( A. x x = y -> ( A. y ps -> A. x ps ) ) |
|
| 6 | 4 5 | impbid | |- ( A. x x = y -> ( A. x ps <-> A. y ps ) ) |
| 7 | 3 6 | bitrd | |- ( A. x x = y -> ( A. x ph <-> A. y ps ) ) |