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Theorem mopick 2361
 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 2282 . . 3
2 sp 1808 . . . . 5
3 id 22 . . . . . . . 8
43anim1d 564 . . . . . . 7
54aleximi 1632 . . . . . 6
6 sb56 2154 . . . . . . 7
7 sp 1808 . . . . . . 7
86, 7sylbi 195 . . . . . 6
95, 8syl6 33 . . . . 5
102, 9syl5d 67 . . . 4
1110exlimiv 1698 . . 3
121, 11sylbi 195 . 2
1312imp 429 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369  wal 1377  wex 1596  wmo 2276 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-12 1803  ax-13 1968 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1597  df-nf 1600  df-eu 2279  df-mo 2280 This theorem is referenced by:  eupick  2364  mopick2  2370  moexex  2371  moexexOLD  2372  morex  3287  imadif  5661  cmetss  21488
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