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Theorem 2moex 2034
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 1429 . . 3 (∃𝑦𝜑 → ∀𝑦𝑦𝜑)
21hbmo 1987 . 2 (∃*𝑥𝑦𝜑 → ∀𝑦∃*𝑥𝑦𝜑)
3 19.8a 1527 . . 3 (𝜑 → ∃𝑦𝜑)
43moimi 2013 . 2 (∃*𝑥𝑦𝜑 → ∃*𝑥𝜑)
52, 4alrimih 1403 1 (∃*𝑥𝑦𝜑 → ∀𝑦∃*𝑥𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1287  wex 1426  ∃*wmo 1949
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 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-eu 1951  df-mo 1952
This theorem is referenced by:  2rmorex  2819
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