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Theorem mopick 2343
 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 1629 . . . 4
2 nfs1v 2182 . . . . 5
3 nfs1v 2182 . . . . 5
42, 3nfan 1846 . . . 4
5 sbequ12 1944 . . . . 5
6 sbequ12 1944 . . . . 5
75, 6anbi12d 692 . . . 4
81, 4, 7cbvex 1983 . . 3
9 nfv 1629 . . . . . . 7
109mo3 2312 . . . . . 6
11 sp 1763 . . . . . . 7
1211sps 1770 . . . . . 6
1310, 12sylbi 188 . . . . 5
14 sbequ2 1660 . . . . . . . . 9
1514imim2i 14 . . . . . . . 8
1615exp3a 426 . . . . . . 7
1716com4t 81 . . . . . 6
1817imp 419 . . . . 5
1913, 18syl5 30 . . . 4
2019exlimiv 1644 . . 3
218, 20sylbi 188 . 2
2221impcom 420 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359  wal 1549  wex 1550  wsb 1658  wmo 2282 This theorem is referenced by:  eupick  2344  mopick2  2348  moexex  2350  morex  3118  imadif  5528  cmetss  19267 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286
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