Description: Bound-variable hypothesis builder for the unique existential quantifier. Deduction version of nfeu . Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker nfeudw when possible. (Contributed by NM, 15-Feb-2013) (Revised by Mario Carneiro, 7-Oct-2016) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | nfeud.1 | |- F/ y ph |
|
| nfeud.2 | |- ( ph -> F/ x ps ) |
||
| Assertion | nfeud | |- ( ph -> F/ x E! y ps ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nfeud.1 | |- F/ y ph |
|
| 2 | nfeud.2 | |- ( ph -> F/ x ps ) |
|
| 3 | 2 | adantr | |- ( ( ph /\ -. A. x x = y ) -> F/ x ps ) |
| 4 | 1 3 | nfeud2 | |- ( ph -> F/ x E! y ps ) |