Description: Alternate version of nfeu1 with a shorter proof but using ax-12 . Bound-variable hypothesis builder for uniqueness. See also nfeu1 . (Contributed by NM, 9-Jul-1994) (Revised by Mario Carneiro, 7-Oct-2016) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | nfeu1ALT | |- F/ x E! x ph |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | eu6 | |- ( E! x ph <-> E. y A. x ( ph <-> x = y ) ) |
|
| 2 | nfexa2 | |- F/ x E. y A. x ( ph <-> x = y ) |
|
| 3 | 1 2 | nfxfr | |- F/ x E! x ph |