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Theorem moanimv 2201
Description: Introduction of a conjunct into "at most one" quantifier. (Contributed by NM, 23-Mar-1995.)
Assertion
Ref Expression
moanimv  |-  ( E* x ( ph  /\  ps )  <->  ( ph  ->  E* x ps ) )
Distinct variable group:    ph, x
Allowed substitution hint:    ps( x)

Proof of Theorem moanimv
StepHypRef Expression
1 nfv 1605 . 2  |-  F/ x ph
21moanim 2199 1  |-  ( E* x ( ph  /\  ps )  <->  ( ph  ->  E* x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ wa 358   E*wmo 2144
This theorem is referenced by:  2reuswap  2967  2reu5lem2  2971  funmo  5271  funcnv  5310  fncnv  5314  isarep2  5332  fnres  5360  fnopabg  5367  fvopab3ig  5599  opabex  5744  zfrep6  5748  fnoprabg  5945  oprabexd  5960  oprabex  5961  ovidi  5966  ovig  5969  caovmo  6057  th3qcor  6766  nqerf  8554  perfdvf  19253  taylf  19740  2reuswap2  23137  abrexdomjm  23165  mptfnf  23226  abrexdom  26405  2rmoswap  27962
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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