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Mirrors > Home > ILE Home > Th. List > nfeu | GIF version |
Description: Bound-variable hypothesis builder for existential uniqueness. Note that x and y needn't be distinct. (Contributed by NM, 8-Mar-1995.) (Revised by Mario Carneiro, 7-Oct-2016.) (Proof rewritten by Jim Kingdon, 23-May-2018.) |
Ref | Expression |
---|---|
nfeu.1 | ⊢ Ⅎxφ |
Ref | Expression |
---|---|
nfeu | ⊢ Ⅎx∃!yφ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1418 | . . 3 ⊢ Ⅎzφ | |
2 | 1 | sb8eu 1910 | . 2 ⊢ (∃!yφ ↔ ∃!z[z / y]φ) |
3 | nfeu.1 | . . . 4 ⊢ Ⅎxφ | |
4 | 3 | nfsb 1819 | . . 3 ⊢ Ⅎx[z / y]φ |
5 | 4 | nfeuv 1915 | . 2 ⊢ Ⅎx∃!z[z / y]φ |
6 | 2, 5 | nfxfr 1360 | 1 ⊢ Ⅎx∃!yφ |
Colors of variables: wff set class |
Syntax hints: Ⅎwnf 1346 [wsb 1642 ∃!weu 1897 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 |
This theorem depends on definitions: df-bi 110 df-tru 1245 df-nf 1347 df-sb 1643 df-eu 1900 |
This theorem is referenced by: hbeu 1918 eusv2nf 4154 |
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