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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:   ,   ,   ,
Allowed substitution hints:   ()   ()

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 1614 . 2
75, 6syl6ibr 227 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 369  wal 1393   wceq 1395  wex 1613   wcel 1819 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111 This theorem is referenced by:  hashf1rn  12428  cshwsexa  12804  wwlktovfo  12908  uvcendim  19009  wlkiswwlk2  24824  wlknwwlknsur  24839  wlkiswwlksur  24846  wwlkextsur  24858  clwlkisclwwlklem2  24913  clwlksizeeq  24979
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