Description: Equality theorem for the non-freeness predicate. (Contributed by Mario Carneiro, 11-Aug-2016) df-nf changed. (Revised by Wolf Lammen, 12-Sep-2021)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | nfbii.1 | |- ( ph <-> ps ) |
|
| Assertion | nfbii | |- ( F/ x ph <-> F/ x ps ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nfbii.1 | |- ( ph <-> ps ) |
|
| 2 | nfbiit | |- ( A. x ( ph <-> ps ) -> ( F/ x ph <-> F/ x ps ) ) |
|
| 3 | 2 1 | mpg | |- ( F/ x ph <-> F/ x ps ) |