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Theorem eu2 2279
 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 2277 . . 3
2 eu2.1 . . . . 5
32eumo0 2278 . . . 4
42mo 2276 . . . 4
53, 4sylib 189 . . 3
61, 5jca 519 . 2
7 19.29r 1604 . . . 4
8 impexp 434 . . . . . . . . 9
98albii 1572 . . . . . . . 8
10219.21 1810 . . . . . . . 8
119, 10bitri 241 . . . . . . 7
1211anbi2i 676 . . . . . 6
13 abai 771 . . . . . 6
1412, 13bitr4i 244 . . . . 5
1514exbii 1589 . . . 4
167, 15sylib 189 . . 3
172eu1 2275 . . 3
1816, 17sylibr 204 . 2
196, 18impbii 181 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1546  wex 1547  wnf 1550  wsb 1655  weu 2254 This theorem is referenced by:  eu3  2280  bm1.1  2389  reu2  3082  bnj1321  29102 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2258
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