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Theorem spc2egv 3168
 Description: Existential specialization with two 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 3091 . . . 4
2 elisset 3091 . . . 4
31, 2anim12i 568 . . 3
4 eeanv 2047 . . 3
53, 4sylibr 215 . 2
6 spc2egv.1 . . . 4
76biimprcd 228 . . 3
872eximdv 1760 . 2
95, 8syl5com 31 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370   wceq 1437  wex 1657   wcel 1872 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-ext 2401 This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-v 3082 This theorem is referenced by:  spc2gv  3169  spc2ev  3174  tpres  6132  addsrpr  9506  mulsrpr  9507  0pthonv  25309  1pthon2v  25321  2pthon3v  25332  usg2wlk  25343  usg2wlkon  25344  dvnprodlem1  37761
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