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Theorem moexexv 2725
 Description: "At most one" double quantification. Usage of this theorem is discouraged because it depends on ax-13 2391. Use the weaker moexexvw 2714 when possible. (Contributed by NM, 26-Jan-1997.) (New usage is discouraged.)
Assertion
Ref Expression
moexexv ((∃*𝑥𝜑 ∧ ∀𝑥∃*𝑦𝜓) → ∃*𝑦𝑥(𝜑𝜓))
Distinct variable group:   𝜑,𝑦
Allowed substitution hints:   𝜑(𝑥)   𝜓(𝑥,𝑦)

Proof of Theorem moexexv
StepHypRef Expression
1 nfv 1915 . 2 𝑦𝜑
21moexex 2724 1 ((∃*𝑥𝜑 ∧ ∀𝑥∃*𝑦𝜓) → ∃*𝑦𝑥(𝜑𝜓))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 399  ∀wal 1536  ∃wex 1781  ∃*wmo 2620 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-10 2145  ax-11 2161  ax-12 2178  ax-13 2391 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-mo 2622 This theorem is referenced by: (None)
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