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Theorem moanmo 2019
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 1954 . . . 4 𝑥∃*𝑥𝜑
32moanim 2016 . . 3 (∃*𝑥(∃*𝑥𝜑𝜑) ↔ (∃*𝑥𝜑 → ∃*𝑥𝜑))
41, 3mpbir 144 . 2 ∃*𝑥(∃*𝑥𝜑𝜑)
5 ancom 262 . . 3 ((𝜑 ∧ ∃*𝑥𝜑) ↔ (∃*𝑥𝜑𝜑))
65mobii 1979 . 2 (∃*𝑥(𝜑 ∧ ∃*𝑥𝜑) ↔ ∃*𝑥(∃*𝑥𝜑𝜑))
74, 6mpbir 144 1 ∃*𝑥(𝜑 ∧ ∃*𝑥𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  ∃*wmo 1943
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-eu 1945  df-mo 1946
This theorem is referenced by: (None)
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