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Theorem 2moex 2692
 Description: Double quantification with "at most one." (Contributed by NM, 3-Dec-2001.)
Assertion
Ref Expression
2moex (∃*𝑥𝑦𝜑 → ∀𝑦∃*𝑥𝜑)

Proof of Theorem 2moex
StepHypRef Expression
1 nfe1 2183 . . 3 𝑦𝑦𝜑
21nfmo 2635 . 2 𝑦∃*𝑥𝑦𝜑
3 19.8a 2206 . . 3 (𝜑 → ∃𝑦𝜑)
43moimi 2669 . 2 (∃*𝑥𝑦𝜑 → ∃*𝑥𝜑)
52, 4alrimi 2238 1 (∃*𝑥𝑦𝜑 → ∀𝑦∃*𝑥𝜑)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1629  ∃wex 1852  ∃*wmo 2619 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-10 2174  ax-11 2190  ax-12 2203  ax-13 2408 This theorem depends on definitions:  df-bi 197  df-an 383  df-or 835  df-tru 1634  df-ex 1853  df-nf 1858  df-eu 2622  df-mo 2623 This theorem is referenced by:  2eu2  2703  2eu5  2706
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