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Theorem moaneu 2263
 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 2244 . . 3 (∃!xφ∃*xφ)
2 nfeu1 2214 . . . 4 x∃!xφ
32moanim 2260 . . 3 (∃*x(∃!xφ φ) ↔ (∃!xφ∃*xφ))
41, 3mpbir 200 . 2 ∃*x(∃!xφ φ)
5 ancom 437 . . 3 ((φ ∃!xφ) ↔ (∃!xφ φ))
65mobii 2240 . 2 (∃*x(φ ∃!xφ) ↔ ∃*x(∃!xφ φ))
74, 6mpbir 200 1 ∃*x(φ ∃!xφ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358  ∃!weu 2204  ∃*wmo 2205 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209 This theorem is referenced by: (None)
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