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Theorem moanmo 2561
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 22 . . 3 (∃*𝑥𝜑 → ∃*𝑥𝜑)
2 nfmo1 2509 . . . 4 𝑥∃*𝑥𝜑
32moanim 2558 . . 3 (∃*𝑥(∃*𝑥𝜑𝜑) ↔ (∃*𝑥𝜑 → ∃*𝑥𝜑))
41, 3mpbir 221 . 2 ∃*𝑥(∃*𝑥𝜑𝜑)
5 ancom 465 . . 3 ((𝜑 ∧ ∃*𝑥𝜑) ↔ (∃*𝑥𝜑𝜑))
65mobii 2521 . 2 (∃*𝑥(𝜑 ∧ ∃*𝑥𝜑) ↔ ∃*𝑥(∃*𝑥𝜑𝜑))
74, 6mpbir 221 1 ∃*𝑥(𝜑 ∧ ∃*𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  ∃*wmo 2499
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-10 2059  ax-11 2074  ax-12 2087
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-eu 2502  df-mo 2503
This theorem is referenced by:  moaneu  2562
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