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Theorem euf 2289
 Description: A version of the existential uniqueness definition with a hypothesis instead of a distinct variable condition. (Contributed by NM, 12-Aug-1993.)
Hypothesis
Ref Expression
euf.1
Assertion
Ref Expression
euf
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem euf
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-eu 2287 . 2
2 euf.1 . . . . 5
3 nfv 1630 . . . . 5
42, 3nfbi 1857 . . . 4
54nfal 1865 . . 3
6 nfv 1630 . . . . 5
7 nfv 1630 . . . . 5
86, 7nfbi 1857 . . . 4
98nfal 1865 . . 3
10 equequ2 1699 . . . . 5
1110bibi2d 311 . . . 4
1211albidv 1636 . . 3
135, 9, 12cbvex 1984 . 2
141, 13bitri 242 1
 Colors of variables: wff set class Syntax hints:   wb 178  wal 1550  wex 1551  wnf 1554  weu 2283 This theorem is referenced by:  eu1  2304  eumo0  2307 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-eu 2287
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