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Theorem rspcimedv 3212
Description: Restricted existential specialization, using implicit substitution. (Contributed by Mario Carneiro, 4-Jan-2017.)
Hypotheses
Ref Expression
rspcimdv.1
rspcimedv.2
Assertion
Ref Expression
rspcimedv
Distinct variable groups:   ,   ,   ,   ,

Proof of Theorem rspcimedv
StepHypRef Expression
1 rspcimdv.1 . . . 4
2 rspcimedv.2 . . . . 5
32con3d 133 . . . 4
41, 3rspcimdv 3211 . . 3
54con2d 115 . 2
6 dfrex2 2908 . 2
75, 6syl6ibr 227 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  /\wa 369  =wceq 1395  e.wcel 1818  A.wral 2807  E.wrex 2808
This theorem is referenced by:  rspcedv  3214  scshwfzeqfzo  12794  symgfixfo  16464  slesolex  19184  clwlkfoclwwlk  24845  el2wlkonot  24869  el2spthonot  24870  el2wlkonotot0  24872  usg2spot2nb  25065  usgra2pthlem1  32353
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-ral 2812  df-rex 2813  df-v 3111
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