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Theorem 2moex 2632
Description: Double quantification with "at most one". Usage of this theorem is discouraged because it depends on ax-13 2367. Use the weaker 2moexv 2619 when possible. (Contributed by NM, 3-Dec-2001.) (New usage is discouraged.)
Assertion
Ref Expression
2moex (∃*𝑥𝑦𝜑 → ∀𝑦∃*𝑥𝜑)

Proof of Theorem 2moex
StepHypRef Expression
1 nfe1 2140 . . 3 𝑦𝑦𝜑
21nfmo 2552 . 2 𝑦∃*𝑥𝑦𝜑
3 19.8a 2170 . . 3 (𝜑 → ∃𝑦𝜑)
43moimi 2535 . 2 (∃*𝑥𝑦𝜑 → ∃*𝑥𝜑)
52, 4alrimi 2202 1 (∃*𝑥𝑦𝜑 → ∀𝑦∃*𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1532  wex 1774  ∃*wmo 2528
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-10 2130  ax-11 2147  ax-12 2167  ax-13 2367
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-tru 1537  df-ex 1775  df-nf 1779  df-mo 2530
This theorem is referenced by:  2eu2  2644
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