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Theorem moanim 2358
 Description: Introduction of a conjunct into "at most one" quantifier. (Contributed by NM, 3-Dec-2001.) (Proof shortened by Wolf Lammen, 24-Dec-2018.)
Hypothesis
Ref Expression
moanim.1
Assertion
Ref Expression
moanim

Proof of Theorem moanim
StepHypRef Expression
1 moanim.1 . . . 4
2 ibar 507 . . . 4
31, 2mobid 2318 . . 3
43biimprcd 229 . 2
5 simpl 459 . . . . . 6
61, 5exlimi 1995 . . . . 5
7 exmo 2324 . . . . . 6
87ori 377 . . . . 5
96, 8nsyl4 148 . . . 4
109con1i 133 . . 3
11 moan 2353 . . 3
1210, 11ja 165 . 2
134, 12impbii 191 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 188   wa 371  wex 1663  wnf 1667  wmo 2300 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-12 1933 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-ex 1664  df-nf 1668  df-eu 2303  df-mo 2304 This theorem is referenced by:  moanimv  2360  moanmo  2361
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