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Theorem eu2 2326
Description: An alternate way of defining existential uniqueness. Definition 6.10 of [TakeutiZaring] p. 26. (Contributed by NM, 8-Jul-1994.) (Proof shortened by Wolf Lammen, 2-Dec-2018.)
Hypothesis
Ref Expression
eu2.1
Assertion
Ref Expression
eu2
Distinct variable group:   ,

Proof of Theorem eu2
StepHypRef Expression
1 eu5 2310 . 2
2 eu2.1 . . . 4
32mo3 2323 . . 3
43anbi2i 694 . 2
51, 4bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  E.wex 1612  F/wnf 1616  [wsb 1739  E!weu 2282  E*wmo 2283
This theorem is referenced by:  eu3OLD  2329  bm1.1OLD  2441  reu2  3287  bnj1321  34083
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-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287
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