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Theorem 2moex 2028
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 hbe1 1425 . . 3 (∃𝑦𝜑 → ∀𝑦𝑦𝜑)
21hbmo 1981 . 2 (∃*𝑥𝑦𝜑 → ∀𝑦∃*𝑥𝑦𝜑)
3 19.8a 1523 . . 3 (𝜑 → ∃𝑦𝜑)
43moimi 2007 . 2 (∃*𝑥𝑦𝜑 → ∃*𝑥𝜑)
52, 4alrimih 1399 1 (∃*𝑥𝑦𝜑 → ∀𝑦∃*𝑥𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1283  wex 1422  ∃*wmo 1943
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-eu 1945  df-mo 1946
This theorem is referenced by:  2rmorex  2797
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