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Theorem mopick 2356
 Description: "At most one" picks a variable value, eliminating an existential quantifier. (Contributed by NM, 27-Jan-1997.) (Proof shortened by Wolf Lammen, 17-Sep-2019.)
Assertion
Ref Expression
mopick

Proof of Theorem mopick
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 mo2v 2289 . . 3
2 sp 1859 . . . . 5
3 pm3.45 834 . . . . . . 7
43aleximi 1653 . . . . . 6
5 sb56 2172 . . . . . . 7
6 sp 1859 . . . . . . 7
75, 6sylbi 195 . . . . . 6
84, 7syl6 33 . . . . 5
92, 8syl5d 67 . . . 4
109exlimiv 1722 . . 3
111, 10sylbi 195 . 2
1211imp 429 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  A.wal 1393  E.wex 1612  E*wmo 2283 This theorem is referenced by:  eupick  2358  mopick2  2362  moexex  2363  morex  3283  imadif  5668  cmetss  21753 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  ax-13 1999 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-eu 2286  df-mo 2287
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