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Theorem eu2 2229
 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 2227 . . 3
2 eu2.1 . . . . 5
32eumo0 2228 . . . 4
42mo 2226 . . . 4
53, 4sylib 188 . . 3
61, 5jca 518 . 2
7 19.29r 1597 . . . 4
8 impexp 433 . . . . . . . . 9
98albii 1566 . . . . . . . 8
10219.21 1796 . . . . . . . 8
119, 10bitri 240 . . . . . . 7
1211anbi2i 675 . . . . . 6
13 abai 770 . . . . . 6
1412, 13bitr4i 243 . . . . 5
1514exbii 1582 . . . 4
167, 15sylib 188 . . 3
172eu1 2225 . . 3
1816, 17sylibr 203 . 2
196, 18impbii 180 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wal 1540  wex 1541  wnf 1544  wsb 1648  weu 2204 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208 This theorem is referenced by:  eu3  2230  bm1.1  2338  reu2  3024
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