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Theorem moexexv 2639
Description: "At most one" double quantification. Usage of this theorem is discouraged because it depends on ax-13 2377. Use the weaker moexexvw 2628 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 1914 . 2 𝑦𝜑
21moexex 2638 1 ((∃*𝑥𝜑 ∧ ∀𝑥∃*𝑦𝜓) → ∃*𝑦𝑥(𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395  wal 1538  wex 1779  ∃*wmo 2538
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-10 2141  ax-11 2157  ax-12 2177  ax-13 2377
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1543  df-ex 1780  df-nf 1784  df-mo 2540
This theorem is referenced by: (None)
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