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Theorem moanmo 2684
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 2616 . . . 4 𝑥∃*𝑥𝜑
32moanim 2682 . . 3 (∃*𝑥(∃*𝑥𝜑𝜑) ↔ (∃*𝑥𝜑 → ∃*𝑥𝜑))
41, 3mpbir 234 . 2 ∃*𝑥(∃*𝑥𝜑𝜑)
5 ancom 464 . . 3 ((𝜑 ∧ ∃*𝑥𝜑) ↔ (∃*𝑥𝜑𝜑))
65mobii 2606 . 2 (∃*𝑥(𝜑 ∧ ∃*𝑥𝜑) ↔ ∃*𝑥(∃*𝑥𝜑𝜑))
74, 6mpbir 234 1 ∃*𝑥(𝜑 ∧ ∃*𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399  ∃*wmo 2596
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-10 2142  ax-11 2158  ax-12 2175
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-nf 1786  df-mo 2598
This theorem is referenced by:  moaneu  2685
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