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Theorem euf 2292
Description: A version of the existential uniqueness definition with a hypothesis instead of a distinct variable condition. (Contributed by NM, 12-Aug-1993.) (Proof shortened by Wolf Lammen, 30-Oct-2018.)
Hypothesis
Ref Expression
euf.1
Assertion
Ref Expression
euf
Distinct variable group:   ,

Proof of Theorem euf
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-eu 2286 . 2
2 euf.1 . . . . 5
3 nfv 1707 . . . . 5
42, 3nfbi 1934 . . . 4
54nfal 1947 . . 3
6 nfv 1707 . . 3
7 equequ2 1799 . . . . 5
87bibi2d 318 . . . 4
98albidv 1713 . . 3
105, 6, 9cbvex 2022 . 2
111, 10bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  A.wal 1393  E.wex 1612  F/wnf 1616  E!weu 2282
This theorem is referenced by:  eumo0OLD  2317  eu1  2327  bj-eumo0  34414
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-eu 2286
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