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Theorem spc2egv 2636
Description: Existential specialization with 2 quantifiers, using implicit substitution. (Contributed by NM, 3-Aug-1995.)
Hypothesis
Ref Expression
spc2egv.1
Assertion
Ref Expression
spc2egv  V  W
Distinct variable groups:   ,,   ,,   ,,
Allowed substitution hints:   (,)    V(,)    W(,)

Proof of Theorem spc2egv
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 . . . 4
76biimprcd 149 . . 3
872eximdv 1759 . 2
95, 8syl5com 26 1  V  W
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98   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:  spc2ev  2642  th3q  6147  addnnnq0  6432  mulnnnq0  6433  addsrpr  6673  mulsrpr  6674
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