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Theorem spc2egv 3196
 Description: Existential specialization with 2 quantifiers, using implicit substitution. (Contributed by NM, 3-Aug-1995.)
Hypothesis
Ref Expression
spc2egv.1
Assertion
Ref Expression
spc2egv
Distinct variable groups:   ,,   ,,   ,,

Proof of Theorem spc2egv
StepHypRef Expression
1 elisset 3120 . . . 4
2 elisset 3120 . . . 4
31, 2anim12i 566 . . 3
4 eeanv 1988 . . 3
53, 4sylibr 212 . 2
6 spc2egv.1 . . . 4
76biimprcd 225 . . 3
872eximdv 1712 . 2
95, 8syl5com 30 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  E.wex 1612  e.wcel 1818 This theorem is referenced by:  spc2gv  3197  spc2ev  3202  addsrpr  9473  mulsrpr  9474  0pthonv  24583  1pthon2v  24595  2pthon3v  24606  usg2wlk  24617  usg2wlkon  24618  dvnprodlem1  31743  tpres  32554 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111
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