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Theorem moanimv 2101
Description: Introduction of a conjunct into at-most-one quantifier. (Contributed by NM, 23-Mar-1995.)
Assertion
Ref Expression
moanimv (∃*𝑥(𝜑𝜓) ↔ (𝜑 → ∃*𝑥𝜓))
Distinct variable group:   𝜑,𝑥
Allowed substitution hint:   𝜓(𝑥)

Proof of Theorem moanimv
StepHypRef Expression
1 nfv 1528 . 2 𝑥𝜑
21moanim 2100 1 (∃*𝑥(𝜑𝜓) ↔ (𝜑 → ∃*𝑥𝜓))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104  wb 105  ∃*wmo 2027
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535
This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-eu 2029  df-mo 2030
This theorem is referenced by:  mosubt  2915  2reuswapdc  2942  2rmorex  2944  mosubopt  4692  funmo  5232  funcnv  5278  fncnv  5283  isarep2  5304  fnres  5333  fnopabg  5340  fvopab3ig  5591  opabex  5741  fnoprabg  5976  ovidi  5993  ovig  5996  oprabexd  6128  oprabex  6129  th3qcor  6639  dvfgg  14160
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