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Theorem spc2gv 2643
 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 2568 . . . 4
2 elisset 2568 . . . 4
31, 2anim12i 321 . . 3
4 eeanv 1807 . . 3
53, 4sylibr 137 . 2
6 spc2egv.1 . . . . . 6
76biimpcd 148 . . . . 5
872alimi 1345 . . . 4
9 exim 1490 . . . . 5
109alimi 1344 . . . 4
11 exim 1490 . . . 4
128, 10, 113syl 17 . . 3
13 19.9v 1751 . . . 4
14 19.9v 1751 . . . 4
1513, 14bitri 173 . . 3
1612, 15syl6ib 150 . 2
175, 16syl5com 26 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98  wal 1241   wceq 1243  wex 1381   wcel 1393 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-v 2559 This theorem is referenced by:  trel  3861  elovmpt2  5701
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