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Theorem spc2egv 3038
 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:   ,,   ,,   ,,
Allowed substitution hints:   (,)   (,)   (,)

Proof of Theorem spc2egv
StepHypRef Expression
1 elisset 2966 . . . 4
2 elisset 2966 . . . 4
31, 2anim12i 550 . . 3
4 eeanv 1937 . . 3
53, 4sylibr 204 . 2
6 spc2egv.1 . . . 4
76biimprcd 217 . . 3
872eximdv 1634 . 2
95, 8syl5com 28 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wex 1550   wceq 1652   wcel 1725 This theorem is referenced by:  spc2gv  3039  spc2ev  3044  th3q  7013  0pthonv  21581  1pthon2v  21593  2pthon3v  21604  usg2wlk  28319  usg2wlkon  28320 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-v 2958
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