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Theorem 2moex 2392
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 1935 . . 3  |-  F/ y E. y ph
21nfmo 2336 . 2  |-  F/ y E* x E. y ph
3 19.8a 1955 . . 3  |-  ( ph  ->  E. y ph )
43moimi 2369 . 2  |-  ( E* x E. y ph  ->  E* x ph )
52, 4alrimi 1975 1  |-  ( E* x E. y ph  ->  A. y E* x ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1450   E.wex 1671   E*wmo 2320
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104
This theorem depends on definitions:  df-bi 190  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-eu 2323  df-mo 2324
This theorem is referenced by:  2eu2  2403  2eu5  2406
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