Description: If x is not free in ph , it is not free in E. y ph . (Contributed by NM, 12-Mar-1993) Reduce symbol count in nfex , hbex . (Revised by Wolf Lammen, 16-Oct-2021)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | hbex.1 | |- ( ph -> A. x ph ) |
|
| Assertion | hbex | |- ( E. y ph -> A. x E. y ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | hbex.1 | |- ( ph -> A. x ph ) |
|
| 2 | 1 | nf5i | |- F/ x ph |
| 3 | 2 | nfex | |- F/ x E. y ph |
| 4 | 3 | nf5ri | |- ( E. y ph -> A. x E. y ph ) |