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Theorem rspcimedv 2658
 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:   ,   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem rspcimedv
StepHypRef Expression
1 rspcimdv.1 . . 3
2 simpr 103 . . . . . . 7
32eleq1d 2106 . . . . . 6
43biimprd 147 . . . . 5
5 rspcimedv.2 . . . . 5
64, 5anim12d 318 . . . 4
71, 6spcimedv 2639 . . 3
81, 7mpand 405 . 2
9 df-rex 2312 . 2
108, 9syl6ibr 151 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wceq 1243  wex 1381   wcel 1393  wrex 2307 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-v 2559 This theorem is referenced by:  rspcedv  2660
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