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Theorem spc2gv 2697
 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 2622 . . . 4
2 elisset 2622 . . . 4
31, 2anim12i 331 . . 3
4 eeanv 1850 . . 3
53, 4sylibr 132 . 2
6 spc2egv.1 . . . . . 6
76biimpcd 157 . . . . 5
872alimi 1386 . . . 4
9 exim 1531 . . . . 5
109alimi 1385 . . . 4
11 exim 1531 . . . 4
128, 10, 113syl 17 . . 3
13 19.9v 1794 . . . 4
14 19.9v 1794 . . . 4
1513, 14bitri 182 . . 3
1612, 15syl6ib 159 . 2
175, 16syl5com 29 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wb 103  wal 1283   wceq 1285  wex 1422   wcel 1434 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-ext 2065 This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-v 2612 This theorem is referenced by:  rspc2gv  2720  trel  3902  exmidundif  3991  elovmpt2  5752
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