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Theorem moanim 2350
 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 504 . . . 4
31, 2mobid 2303 . . 3
43biimprcd 225 . 2
5 simpl 457 . . . . . 6
61, 5exlimi 1912 . . . . 5
7 exmo 2309 . . . . . 6
87ori 375 . . . . 5
96, 8nsyl4 142 . . . 4
109con1i 129 . . 3
11 moan 2345 . . 3
1210, 11ja 161 . 2
134, 12impbii 188 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  E.wex 1612  F/wnf 1616  E*wmo 2283 This theorem is referenced by:  moanimv  2352  moanmo  2353  2eu1OLD  2377 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-ex 1613  df-nf 1617  df-eu 2286  df-mo 2287
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