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Theorem 2moex 2214
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 1706 . . 3  |-  F/ y E. y ph
21nfmo 2160 . 2  |-  F/ y E* x E. y ph
3 19.8a 1718 . . 3  |-  ( ph  ->  E. y ph )
43moimi 2190 . 2  |-  ( E* x E. y ph  ->  E* x ph )
52, 4alrimi 1745 1  |-  ( E* x E. y ph  ->  A. y E* x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1527   E.wex 1528   E*wmo 2144
This theorem is referenced by:  2eu2  2224  2eu5  2227
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148
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