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Theorem spc2ev 3044
 Description: Existential specialization, using implicit substitution. (Contributed by NM, 3-Aug-1995.)
Hypotheses
Ref Expression
spc2ev.1
spc2ev.2
spc2ev.3
Assertion
Ref Expression
spc2ev
Distinct variable groups:   ,,   ,,   ,,
Allowed substitution hints:   (,)

Proof of Theorem spc2ev
StepHypRef Expression
1 spc2ev.1 . 2
2 spc2ev.2 . 2
3 spc2ev.3 . . 3
43spc2egv 3038 . 2
51, 2, 4mp2an 654 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wex 1550   wceq 1652   wcel 1725  cvv 2956 This theorem is referenced by:  relop  5023  th3qlem2  7011  endisj  7195  dcomex  8327  axcnre  9039  constr3cyclpe  21650  3v3e3cycl2  21651  qqhval2  24366  itg2addnclem3  26258 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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