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Theorem spc2gv 2800
 Description: Specialization with 2 quantifiers, using implicit substitution. (Contributed by NM, 27-Apr-2004.)
Hypothesis
Ref Expression
spc2egv.1
Assertion
Ref Expression
spc2gv
Distinct variable groups:   ,,   ,,   ,,
Allowed substitution hints:   (,)   (,)   (,)

Proof of Theorem spc2gv
StepHypRef Expression
1 elisset 2723 . . . 4
2 elisset 2723 . . . 4
31, 2anim12i 336 . . 3
4 eeanv 1909 . . 3
53, 4sylibr 133 . 2
6 spc2egv.1 . . . . . 6
76biimpcd 158 . . . . 5
872alimi 1433 . . . 4
9 exim 1576 . . . . 5
109alimi 1432 . . . 4
11 exim 1576 . . . 4
128, 10, 113syl 17 . . 3
13 19.9v 1848 . . . 4
14 19.9v 1848 . . . 4
1513, 14bitri 183 . . 3
1612, 15syl6ib 160 . 2
175, 16syl5com 29 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104  wal 1330   wceq 1332  wex 1469   wcel 2125 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-v 2711 This theorem is referenced by:  rspc2gv  2825  trel  4065  exmidundif  4162  exmidundifim  4163  elovmpo  6011  cnmpt12  12634  cnmpt22  12641  exmidsbthrlem  13542
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