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Theorem spcimedv 3193
Description: Restricted existential specialization, using implicit substitution. (Contributed by Mario Carneiro, 4-Jan-2017.)
Hypotheses
Ref Expression
spcimdv.1
spcimedv.2
Assertion
Ref Expression
spcimedv
Distinct variable groups:   ,   ,   ,

Proof of Theorem spcimedv
StepHypRef Expression
1 spcimdv.1 . . . 4
2 spcimedv.2 . . . . 5
32con3d 133 . . . 4
41, 3spcimdv 3191 . . 3
54con2d 115 . 2
6 df-ex 1613 . 2
75, 6syl6ibr 227 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  /\wa 369  A.wal 1393  =wceq 1395  E.wex 1612  e.wcel 1818
This theorem is referenced by:  hashf1rn  12425  cshwsexa  12792  wwlktovfo  12896  uvcendim  18882  wlkiswwlk2  24697  wlknwwlknsur  24712  wlkiswwlksur  24719  wwlkextsur  24731  clwlkisclwwlklem2  24786  clwlksizeeq  24852
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-13 1999  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-nfc 2607  df-v 3111
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