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Theorem nulmoOLD 2758
 Description: Obsolete version of nulmo 2757 as of 26-Apr-2023. (Contributed by NM, 22-Dec-2007.) Use the at-most-one quantifier. (Revised by BJ, 17-Sep-2022.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
nulmoOLD ∃*𝑥𝑦 ¬ 𝑦𝑥
Distinct variable group:   𝑥,𝑦

Proof of Theorem nulmoOLD
StepHypRef Expression
1 nfv 1873 . . 3 𝑥
21axextmo 2756 . 2 ∃*𝑥𝑦(𝑦𝑥 ↔ ⊥)
3 nbfal 1522 . . . . 5 𝑦𝑥 ↔ (𝑦𝑥 ↔ ⊥))
43bicomi 216 . . . 4 ((𝑦𝑥 ↔ ⊥) ↔ ¬ 𝑦𝑥)
54albii 1782 . . 3 (∀𝑦(𝑦𝑥 ↔ ⊥) ↔ ∀𝑦 ¬ 𝑦𝑥)
65mobii 2559 . 2 (∃*𝑥𝑦(𝑦𝑥 ↔ ⊥) ↔ ∃*𝑥𝑦 ¬ 𝑦𝑥)
72, 6mpbi 222 1 ∃*𝑥𝑦 ¬ 𝑦𝑥
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   ↔ wb 198  ∀wal 1505  ⊥wfal 1519  ∃*wmo 2545 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1758  ax-4 1772  ax-5 1869  ax-6 1928  ax-7 1965  ax-9 2059  ax-10 2079  ax-11 2093  ax-12 2106  ax-ext 2751 This theorem depends on definitions:  df-bi 199  df-an 388  df-or 834  df-tru 1510  df-fal 1520  df-ex 1743  df-nf 1747  df-sb 2016  df-mo 2547 This theorem is referenced by: (None)
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