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Theorem nfeu1 2214
 Description: Bound-variable hypothesis builder for uniqueness. (Contributed by NM, 9-Jul-1994.) (Revised by Mario Carneiro, 7-Oct-2016.)
Assertion
Ref Expression
nfeu1 x∃!xφ

Proof of Theorem nfeu1
Dummy variable y is distinct from all other variables.
StepHypRef Expression
1 df-eu 2208 . 2 (∃!xφyx(φx = y))
2 nfa1 1788 . . 3 xx(φx = y)
32nfex 1843 . 2 xyx(φx = y)
41, 3nfxfr 1570 1 x∃!xφ
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176  ∀wal 1540  ∃wex 1541  Ⅎwnf 1544   = wceq 1642  ∃!weu 2204 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545  df-eu 2208 This theorem is referenced by:  nfmo1  2215  moaneu  2263  eupicka  2268  2eu8  2291  exists2  2294  nfreu1  2781  iota2  4367  sniota  4369  fv3  5341  tz6.12c  5347
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