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Theorem moaneu 1973
Description: Nested "at most one" and uniqueness quantifiers. (Contributed by NM, 25-Jan-2006.)
Assertion
Ref Expression
moaneu ∃*x(φ ∃!xφ)

Proof of Theorem moaneu
StepHypRef Expression
1 eumo 1929 . . 3 (∃!xφ∃*xφ)
2 nfeu1 1908 . . . 4 x∃!xφ
32moanim 1971 . . 3 (∃*x(∃!xφ φ) ↔ (∃!xφ∃*xφ))
41, 3mpbir 134 . 2 ∃*x(∃!xφ φ)
5 ancom 253 . . 3 ((φ ∃!xφ) ↔ (∃!xφ φ))
65mobii 1934 . 2 (∃*x(φ ∃!xφ) ↔ ∃*x(∃!xφ φ))
74, 6mpbir 134 1 ∃*x(φ ∃!xφ)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  ∃!weu 1897  ∃*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: (None)
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