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Theorem 2eu2 2285
Description: Double existential uniqueness. (Contributed by NM, 3-Dec-2001.)
Assertion
Ref Expression
2eu2

Proof of Theorem 2eu2
StepHypRef Expression
1 eumo 2244 . . 3
2 2moex 2275 . . 3
3 2eu1 2284 . . . 4
4 simpl 443 . . . 4
53, 4syl6bi 219 . . 3
61, 2, 53syl 18 . 2
7 2exeu 2281 . . 3
87expcom 424 . 2
96, 8impbid 183 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wb 176   wa 358  wal 1540  wex 1541  weu 2204  wmo 2205
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  df-mo 2209
This theorem is referenced by:  2eu8  2291
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