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Theorem 2moex 1983
 Description: Double quantification with "at most one." (Contributed by NM, 3-Dec-2001.)
Assertion
Ref Expression
2moex (∃*xyφy∃*xφ)

Proof of Theorem 2moex
StepHypRef Expression
1 hbe1 1381 . . 3 (yφyyφ)
21hbmo 1936 . 2 (∃*xyφy∃*xyφ)
3 19.8a 1479 . . 3 (φyφ)
43moimi 1962 . 2 (∃*xyφ∃*xφ)
52, 4alrimih 1355 1 (∃*xyφy∃*xφ)
 Colors of variables: wff set class Syntax hints:   → wi 4  ∀wal 1240  ∃wex 1378  ∃*wmo 1898 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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901 This theorem is referenced by:  2rmorex  2739
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