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Theorem moanmo 1974
Description: Nested "at most one" quantifiers. (Contributed by NM, 25-Jan-2006.)
Assertion
Ref Expression
moanmo ∃*x(φ ∃*xφ)

Proof of Theorem moanmo
StepHypRef Expression
1 id 19 . . 3 (∃*xφ∃*xφ)
2 nfmo1 1909 . . . 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  ∃*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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