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Theorem 2moex 2215
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 1707 . . 3  |-  F/ y E. y ph
21nfmo 2161 . 2  |-  F/ y E* x E. y ph
3 19.8a 1719 . . 3  |-  ( ph  ->  E. y ph )
43moimi 2191 . 2  |-  ( E* x E. y ph  ->  E* x ph )
52, 4alrimi 1746 1  |-  ( E* x E. y ph  ->  A. y E* x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 6   A.wal 1528   E.wex 1529   E*wmo 2145
This theorem is referenced by:  2eu2  2225  2eu5  2228
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1534  ax-5 1545  ax-17 1604  ax-9 1637  ax-8 1645  ax-6 1704  ax-7 1709  ax-11 1716  ax-12 1867
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1312  df-ex 1530  df-nf 1533  df-sb 1632  df-eu 2148  df-mo 2149
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