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Theorem hbeu1 1907
 Description: Bound-variable hypothesis builder for uniqueness. (Contributed by NM, 9-Jul-1994.)
Assertion
Ref Expression
hbeu1 (∃!xφx∃!xφ)

Proof of Theorem hbeu1
Dummy variable y is distinct from all other variables.
StepHypRef Expression
1 df-eu 1900 . 2 (∃!xφyx(φx = y))
2 hba1 1430 . . 3 (x(φx = y) → xx(φx = y))
32hbex 1524 . 2 (yx(φx = y) → xyx(φx = y))
41, 3hbxfrbi 1358 1 (∃!xφx∃!xφ)
 Colors of variables: wff set class Syntax hints:   → wi 4   ↔ wb 98  ∀wal 1240  ∃wex 1378  ∃!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-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-ial 1424 This theorem depends on definitions:  df-bi 110  df-eu 1900 This theorem is referenced by:  hbmo1  1935  eupicka  1977  exists2  1994
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