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Theorem euim 2254
Description: Add existential uniqueness quantifiers to an implication. Note the reversed implication in the antecedent. (Contributed by NM, 19-Oct-2005.) (Proof shortened by Andrew Salmon, 14-Jun-2011.)
Assertion
Ref Expression
euim

Proof of Theorem euim
StepHypRef Expression
1 ax-1 6 . . 3
2 euimmo 2253 . . 3
31, 2anim12ii 553 . 2
4 eu5 2242 . 2
53, 4syl6ibr 218 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   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: (None)
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