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Theorem eu2 2305
 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 2303 . . 3
2 eu2.1 . . . . 5
32eumo0 2304 . . . 4
42mo 2302 . . . 4
53, 4sylib 189 . . 3
61, 5jca 519 . 2
7 19.29r 1607 . . . 4
8 impexp 434 . . . . . . . . 9
98albii 1575 . . . . . . . 8
10219.21 1814 . . . . . . . 8
119, 10bitri 241 . . . . . . 7
1211anbi2i 676 . . . . . 6
13 abai 771 . . . . . 6
1412, 13bitr4i 244 . . . . 5
1514exbii 1592 . . . 4
167, 15sylib 189 . . 3
172eu1 2301 . . 3
1816, 17sylibr 204 . 2
196, 18impbii 181 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549  wex 1550  wnf 1553  wsb 1658  weu 2280 This theorem is referenced by:  eu3  2306  bm1.1  2420  reu2  3114  bnj1321  29250 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284
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