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Theorem 2moex 2083
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 1471 . . 3 (∃𝑦𝜑 → ∀𝑦𝑦𝜑)
21hbmo 2036 . 2 (∃*𝑥𝑦𝜑 → ∀𝑦∃*𝑥𝑦𝜑)
3 19.8a 1569 . . 3 (𝜑 → ∃𝑦𝜑)
43moimi 2062 . 2 (∃*𝑥𝑦𝜑 → ∃*𝑥𝜑)
52, 4alrimih 1445 1 (∃*𝑥𝑦𝜑 → ∀𝑦∃*𝑥𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1329  wex 1468  ∃*wmo 1998
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-eu 2000  df-mo 2001
This theorem is referenced by:  2rmorex  2885
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