Description: Variable substitution in unique existential quantifier. Version of sb8eu requiring more disjoint variables, but fewer axioms. (Contributed by NM, 7-Aug-1994) (Revised by Wolf Lammen, 7-Feb-2023)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | sb8euv.nf | |- F/ y ph |
|
| Assertion | sb8euv | |- ( E! x ph <-> E! y [ y / x ] ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sb8euv.nf | |- F/ y ph |
|
| 2 | 1 | nfsbv | |- F/ y [ w / x ] ph |
| 3 | 2 | sb8eulem | |- ( E! x ph <-> E! y [ y / x ] ph ) |