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Theorem spc2gv 2637
Description: Specialization with 2 quantifiers, using implicit substitution. (Contributed by NM, 27-Apr-2004.)
Hypothesis
Ref Expression
spc2egv.1
Assertion
Ref Expression
spc2gv  V  W
Distinct variable groups:   ,,   ,,   ,,
Allowed substitution hints:   (,)    V(,)    W(,)

Proof of Theorem spc2gv
StepHypRef Expression
1 elisset 2562 . . . 4  V
2 elisset 2562 . . . 4  W
31, 2anim12i 321 . . 3  V  W
4 eeanv 1804 . . 3
53, 4sylibr 137 . 2  V  W
6 spc2egv.1 . . . . . 6
76biimpcd 148 . . . . 5
872alimi 1342 . . . 4
9 exim 1487 . . . . 5
109alimi 1341 . . . 4
11 exim 1487 . . . 4
128, 10, 113syl 17 . . 3
13 19.9v 1748 . . . 4
14 19.9v 1748 . . . 4
1513, 14bitri 173 . . 3
1612, 15syl6ib 150 . 2
175, 16syl5com 26 1  V  W
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  wal 1240   wceq 1242  wex 1378   wcel 1390
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 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-v 2553
This theorem is referenced by:  trel  3852  elovmpt2  5643
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