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Theorem mopick 2266
 Description: "At most one" picks a variable value, eliminating an existential quantifier. (Contributed by NM, 27-Jan-1997.)
Assertion
Ref Expression
mopick

Proof of Theorem mopick
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfv 1619 . . . 4
2 nfs1v 2106 . . . . 5
3 nfs1v 2106 . . . . 5
42, 3nfan 1824 . . . 4
5 sbequ12 1919 . . . . 5
6 sbequ12 1919 . . . . 5
75, 6anbi12d 691 . . . 4
81, 4, 7cbvex 1985 . . 3
9 nfv 1619 . . . . . . 7
109mo3 2235 . . . . . 6
11 sp 1747 . . . . . . 7
1211sps 1754 . . . . . 6
1310, 12sylbi 187 . . . . 5
14 sbequ2 1650 . . . . . . . . 9
1514imim2i 13 . . . . . . . 8
1615exp3a 425 . . . . . . 7
1716com4t 79 . . . . . 6
1817imp 418 . . . . 5
1913, 18syl5 28 . . . 4
2019exlimiv 1634 . . 3
218, 20sylbi 187 . 2
2221impcom 419 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 358  wal 1540  wex 1541   wceq 1642  wsb 1648  wmo 2205 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209 This theorem is referenced by:  eupick  2267  mopick2  2271  moexex  2273  morex  3020  imadif  5171
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