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Theorem 2moex 2342
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 1894 . . 3  |-  F/ y E. y ph
21nfmo 2286 . 2  |-  F/ y E* x E. y ph
3 19.8a 1912 . . 3  |-  ( ph  ->  E. y ph )
43moimi 2319 . 2  |-  ( E* x E. y ph  ->  E* x ph )
52, 4alrimi 1932 1  |-  ( E* x E. y ph  ->  A. y E* x ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1435   E.wex 1657   E*wmo 2270
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057
This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-eu 2273  df-mo 2274
This theorem is referenced by:  2eu2  2353  2eu5  2356
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