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Theorem moanmo 2264
 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 2215 . . . 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  ∃*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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