Description: Bound-variable hypothesis builder for the unique existential quantifier. Note that x and y need not be disjoint. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker nfeuw when possible. (Contributed by NM, 8-Mar-1995) (Revised by Mario Carneiro, 7-Oct-2016) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | nfeu.1 | |- F/ x ph |
|
| Assertion | nfeu | |- F/ x E! y ph |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nfeu.1 | |- F/ x ph |
|
| 2 | nftru | |- F/ y T. |
|
| 3 | 1 | a1i | |- ( T. -> F/ x ph ) |
| 4 | 2 3 | nfeud | |- ( T. -> F/ x E! y ph ) |
| 5 | 4 | mptru | |- F/ x E! y ph |