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Theorem moanimv 2262
 Description: Introduction of a conjunct into "at most one" quantifier. (Contributed by NM, 23-Mar-1995.)
Assertion
Ref Expression
moanimv (∃*x(φ ψ) ↔ (φ∃*xψ))
Distinct variable group:   φ,x
Allowed substitution hint:   ψ(x)

Proof of Theorem moanimv
StepHypRef Expression
1 nfv 1619 . 2 xφ
21moanim 2260 1 (∃*x(φ ψ) ↔ (φ∃*xψ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   ∧ wa 358  ∃*wmo 2205 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209 This theorem is referenced by:  2reuswap  3038  2reu5lem2  3042  funmo  5125  funsn  5147  funcnv  5156  fncnv  5158  fnres  5199  fnopabg  5205  fvopab3ig  5387  fnoprabg  5585  ovidi  5594  ovig  5597
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