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Theorem 2moex 1986
 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 1384 . . 3 (∃𝑦𝜑 → ∀𝑦𝑦𝜑)
21hbmo 1939 . 2 (∃*𝑥𝑦𝜑 → ∀𝑦∃*𝑥𝑦𝜑)
3 19.8a 1482 . . 3 (𝜑 → ∃𝑦𝜑)
43moimi 1965 . 2 (∃*𝑥𝑦𝜑 → ∃*𝑥𝜑)
52, 4alrimih 1358 1 (∃*𝑥𝑦𝜑 → ∀𝑦∃*𝑥𝜑)
 Colors of variables: wff set class Syntax hints:   → wi 4  ∀wal 1241  ∃wex 1381  ∃*wmo 1901 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904 This theorem is referenced by:  2rmorex  2745
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