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Theorem moanimv 2050
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 1491 . 2  |-  F/ x ph
21moanim 2049 1  |-  ( E* x ( ph  /\  ps )  <->  ( ph  ->  E* x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    <-> wb 104   E*wmo 1976
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498
This theorem depends on definitions:  df-bi 116  df-nf 1420  df-sb 1719  df-eu 1978  df-mo 1979
This theorem is referenced by:  mosubt  2832  2reuswapdc  2859  2rmorex  2861  mosubopt  4572  funmo  5106  funcnv  5152  fncnv  5157  isarep2  5178  fnres  5207  fnopabg  5214  fvopab3ig  5461  opabex  5610  fnoprabg  5838  ovidi  5855  ovig  5858  oprabexd  5991  oprabex  5992  th3qcor  6499  dvfgg  12709
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