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Theorem moanmo 2103
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 2038 . . . 4 𝑥∃*𝑥𝜑
32moanim 2100 . . 3 (∃*𝑥(∃*𝑥𝜑𝜑) ↔ (∃*𝑥𝜑 → ∃*𝑥𝜑))
41, 3mpbir 146 . 2 ∃*𝑥(∃*𝑥𝜑𝜑)
5 ancom 266 . . 3 ((𝜑 ∧ ∃*𝑥𝜑) ↔ (∃*𝑥𝜑𝜑))
65mobii 2063 . 2 (∃*𝑥(𝜑 ∧ ∃*𝑥𝜑) ↔ ∃*𝑥(∃*𝑥𝜑𝜑))
74, 6mpbir 146 1 ∃*𝑥(𝜑 ∧ ∃*𝑥𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104  ∃*wmo 2027
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-eu 2029  df-mo 2030
This theorem is referenced by: (None)
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