Description: Substitution of variable in existential quantifier. Version of sb8e with a disjoint variable condition, not requiring ax-13 . (Contributed by NM, 12-Aug-1993) (Revised by Wolf Lammen, 19-Jan-2023)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | sb8v.nf | |- F/ y ph |
|
| Assertion | sb8ev | |- ( E. x ph <-> E. y [ y / x ] ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sb8v.nf | |- F/ y ph |
|
| 2 | nfs1v | |- F/ x [ y / x ] ph |
|
| 3 | sbequ12 | |- ( x = y -> ( ph <-> [ y / x ] ph ) ) |
|
| 4 | 1 2 3 | cbvexv1 | |- ( E. x ph <-> E. y [ y / x ] ph ) |