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Theorem rspcimdv 2956
 Description: Restricted specialization, using implicit substitution. (Contributed by Mario Carneiro, 4-Jan-2017.)
Hypotheses
Ref Expression
rspcimdv.1
rspcimdv.2
Assertion
Ref Expression
rspcimdv
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem rspcimdv
StepHypRef Expression
1 df-ral 2619 . 2
2 rspcimdv.1 . . 3
3 simpr 447 . . . . . . 7
43eleq1d 2419 . . . . . 6
54biimprd 214 . . . . 5
6 rspcimdv.2 . . . . 5
75, 6imim12d 68 . . . 4
82, 7spcimdv 2936 . . 3
92, 8mpid 37 . 2
101, 9syl5bi 208 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 358  wal 1540   wceq 1642   wcel 1710  wral 2614 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-v 2861 This theorem is referenced by:  rspcimedv  2957  rspcdv  2958
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