Description: If x is not free in ph , it is not free in F/ y ph . (Contributed by Mario Carneiro, 11-Aug-2016) (Proof shortened by Wolf Lammen, 30-Dec-2017)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | nfnf.1 | |- F/ x ph |
|
| Assertion | nfnf | |- F/ x F/ y ph |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nfnf.1 | |- F/ x ph |
|
| 2 | df-nf | |- ( F/ y ph <-> ( E. y ph -> A. y ph ) ) |
|
| 3 | 1 | nfex | |- F/ x E. y ph |
| 4 | 1 | nfal | |- F/ x A. y ph |
| 5 | 3 4 | nfim | |- F/ x ( E. y ph -> A. y ph ) |
| 6 | 2 5 | nfxfr | |- F/ x F/ y ph |