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Theorem nfeu 1916
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.)
Hypothesis
Ref Expression
nfeu.1 xφ
Assertion
Ref Expression
nfeu x∃!yφ

Proof of Theorem nfeu
Dummy variable z is distinct from all other variables.
StepHypRef Expression
1 nfv 1418 . . 3 zφ
21sb8eu 1910 . 2 (∃!yφ∃!z[z / y]φ)
3 nfeu.1 . . . 4 xφ
43nfsb 1819 . . 3 x[z / y]φ
54nfeuv 1915 . 2 x∃!z[z / y]φ
62, 5nfxfr 1360 1 x∃!yφ
Colors of variables: wff set class
Syntax hints:  wnf 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-bnd 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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