Description: Bound-variable hypothesis builder for restricted unique existence. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker nfreuw when possible. (Contributed by NM, 30-Oct-2010) (Revised by Mario Carneiro, 8-Oct-2016) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | nfreu.1 | |- F/_ x A |
|
| nfreu.2 | |- F/ x ph |
||
| Assertion | nfreu | |- F/ x E! y e. A ph |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nfreu.1 | |- F/_ x A |
|
| 2 | nfreu.2 | |- F/ x ph |
|
| 3 | nftru | |- F/ y T. |
|
| 4 | 1 | a1i | |- ( T. -> F/_ x A ) |
| 5 | 2 | a1i | |- ( T. -> F/ x ph ) |
| 6 | 3 4 5 | nfreud | |- ( T. -> F/ x E! y e. A ph ) |
| 7 | 6 | mptru | |- F/ x E! y e. A ph |