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Theorem moanimv 2081
 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 1508 . 2 𝑥𝜑
21moanim 2080 1 (∃*𝑥(𝜑𝜓) ↔ (𝜑 → ∃*𝑥𝜓))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 103   ↔ wb 104  ∃*wmo 2007 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 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515 This theorem depends on definitions:  df-bi 116  df-nf 1441  df-sb 1743  df-eu 2009  df-mo 2010 This theorem is referenced by:  mosubt  2889  2reuswapdc  2916  2rmorex  2918  mosubopt  4648  funmo  5182  funcnv  5228  fncnv  5233  isarep2  5254  fnres  5283  fnopabg  5290  fvopab3ig  5539  opabex  5688  fnoprabg  5916  ovidi  5933  ovig  5936  oprabexd  6069  oprabex  6070  th3qcor  6577  dvfgg  13017
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