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Theorem spc3gv 2699
 Description: Specialization with 3 quantifiers, using implicit substitution. (Contributed by NM, 12-May-2008.)
Hypothesis
Ref Expression
spc3egv.1
Assertion
Ref Expression
spc3gv
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,
Allowed substitution hints:   (,,)   (,,)   (,,)   (,,)

Proof of Theorem spc3gv
StepHypRef Expression
1 elisset 2622 . . . 4
2 elisset 2622 . . . 4
3 elisset 2622 . . . 4
41, 2, 33anim123i 1124 . . 3
5 eeeanv 1851 . . 3
64, 5sylibr 132 . 2
7 spc3egv.1 . . . . . . . 8
87biimpcd 157 . . . . . . 7
982alimi 1386 . . . . . 6
109alimi 1385 . . . . 5
11 exim 1531 . . . . . 6
12112alimi 1386 . . . . 5
1310, 12syl 14 . . . 4
14 exim 1531 . . . . 5
1514alimi 1385 . . . 4
16 exim 1531 . . . 4
1713, 15, 163syl 17 . . 3
18 19.9v 1794 . . . 4
19 19.9v 1794 . . . 4
20 19.9v 1794 . . . 4
2118, 19, 203bitri 204 . . 3
2217, 21syl6ib 159 . 2
236, 22syl5com 29 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103   w3a 920  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-3an 922  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-v 2612 This theorem is referenced by:  funopg  4984
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