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Theorem moexexv 2213
Description: "At most one" double quantification. (Contributed by NM, 26-Jan-1997.)
Assertion
Ref Expression
moexexv  |-  ( ( E* x ph  /\  A. x E* y ps )  ->  E* y E. x ( ph  /\  ps ) )
Distinct variable group:    ph, y
Allowed substitution hints:    ph( x)    ps( x, y)

Proof of Theorem moexexv
StepHypRef Expression
1 nfv 1605 . 2  |-  F/ y
ph
21moexex 2212 1  |-  ( ( E* x ph  /\  A. x E* y ps )  ->  E* y E. x ( ph  /\  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358   A.wal 1527   E.wex 1528   E*wmo 2144
This theorem is referenced by:  mosub  2943  funco  5292
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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