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Theorem 2moex 2184
Description: Double quantification with "at most one." (Contributed by NM, 3-Dec-2001.)
Assertion
Ref Expression
2moex  |-  ( E* x E. y ph  ->  A. y E* x ph )

Proof of Theorem 2moex
StepHypRef Expression
1 nfe1 1566 . . 3  |-  F/ y E. y ph
21nfmo 2131 . 2  |-  F/ y E* x E. y ph
3 19.8a 1758 . . 3  |-  ( ph  ->  E. y ph )
43immoi 2160 . 2  |-  ( E* x E. y ph  ->  E* x ph )
52, 4alrimi 1706 1  |-  ( E* x E. y ph  ->  A. y E* x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 6   A.wal 1532   E.wex 1537   E*wmo 2115
This theorem is referenced by:  2eu2  2194  2eu5  2197
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-eu 2118  df-mo 2119
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