Description: The setvar x is not free in F/ x ph . (Contributed by Mario Carneiro, 11-Aug-2016) Remove dependency on ax-12 . (Revised by Wolf Lammen, 12-Oct-2021)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | nfnf1 | |- F/ x F/ x ph |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-nf | |- ( F/ x ph <-> ( E. x ph -> A. x ph ) ) |
|
| 2 | nfe1 | |- F/ x E. x ph |
|
| 3 | nfa1 | |- F/ x A. x ph |
|
| 4 | 2 3 | nfim | |- F/ x ( E. x ph -> A. x ph ) |
| 5 | 1 4 | nfxfr | |- F/ x F/ x ph |