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Theorem eu2 2141
 Description: An alternate way of defining existential uniqueness. Definition 6.10 of [TakeutiZaring] p. 26. (Contributed by NM, 8-Jul-1994.)
Hypothesis
Ref Expression
eu2.1
Assertion
Ref Expression
eu2
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem eu2
StepHypRef Expression
1 euex 2139 . . 3
2 eu2.1 . . . . 5
32eumo0 2140 . . . 4
42mo 2138 . . . 4
53, 4sylib 190 . . 3
61, 5jca 520 . 2
7 19.29r 1596 . . . 4
8 impexp 435 . . . . . . . . 9
98albii 1554 . . . . . . . 8
10219.21 1771 . . . . . . . 8
119, 10bitri 242 . . . . . . 7
1211anbi2i 678 . . . . . 6
13 abai 773 . . . . . 6
1412, 13bitr4i 245 . . . . 5
1514exbii 1580 . . . 4
167, 15sylib 190 . . 3
172eu1 2137 . . 3
1816, 17sylibr 205 . 2
196, 18impbii 182 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178   wa 360  wal 1532  wex 1537  wnf 1539  wsb 1883  weu 2117 This theorem is referenced by:  eu3  2142  bm1.1  2241  reu2  2906  bnj1321  28069 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1927 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884  df-eu 2121
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