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Theorem moexexv 2274
 Description: "At most one" double quantification. (Contributed by NM, 26-Jan-1997.)
Assertion
Ref Expression
moexexv ((∃*xφ x∃*yψ) → ∃*yx(φ ψ))
Distinct variable group:   φ,y
Allowed substitution hints:   φ(x)   ψ(x,y)

Proof of Theorem moexexv
StepHypRef Expression
1 nfv 1619 . 2 yφ
21moexex 2273 1 ((∃*xφ x∃*yψ) → ∃*yx(φ ψ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358  ∀wal 1540  ∃wex 1541  ∃*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:  mosub  3014  funco  5142
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