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Theorem 2eu2 2362
 Description: Double existential uniqueness. (Contributed by NM, 3-Dec-2001.)
Assertion
Ref Expression
2eu2

Proof of Theorem 2eu2
StepHypRef Expression
1 eumo 2321 . . 3
2 2moex 2352 . . 3
3 2eu1 2361 . . . 4
4 simpl 444 . . . 4
53, 4syl6bi 220 . . 3
61, 2, 53syl 19 . 2
7 2exeu 2358 . . 3
87expcom 425 . 2
96, 8impbid 184 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549  wex 1550  weu 2281  wmo 2282 This theorem is referenced by:  2eu8  2368 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 2285  df-mo 2286
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