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Theorem 2moex 2351
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 1747 . . 3  |-  F/ y E. y ph
21nfmo 2297 . 2  |-  F/ y E* x E. y ph
3 19.8a 1762 . . 3  |-  ( ph  ->  E. y ph )
43moimi 2327 . 2  |-  ( E* x E. y ph  ->  E* x ph )
52, 4alrimi 1781 1  |-  ( E* x E. y ph  ->  A. y E* x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1549   E.wex 1550   E*wmo 2281
This theorem is referenced by:  2eu2  2361  2eu5  2364
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 2284  df-mo 2285
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