Description: Obsolete version of nfnbi as of 6-Oct-2024. (Contributed by BJ, 6-May-2019) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | nfnbiOLD | |- ( F/ x ph <-> F/ x -. ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | orcom | |- ( ( A. x ph \/ A. x -. ph ) <-> ( A. x -. ph \/ A. x ph ) ) |
|
| 2 | nf3 | |- ( F/ x ph <-> ( A. x ph \/ A. x -. ph ) ) |
|
| 3 | nf3 | |- ( F/ x -. ph <-> ( A. x -. ph \/ A. x -. -. ph ) ) |
|
| 4 | notnotb | |- ( ph <-> -. -. ph ) |
|
| 5 | 4 | albii | |- ( A. x ph <-> A. x -. -. ph ) |
| 6 | 5 | orbi2i | |- ( ( A. x -. ph \/ A. x ph ) <-> ( A. x -. ph \/ A. x -. -. ph ) ) |
| 7 | 3 6 | bitr4i | |- ( F/ x -. ph <-> ( A. x -. ph \/ A. x ph ) ) |
| 8 | 1 2 7 | 3bitr4i | |- ( F/ x ph <-> F/ x -. ph ) |