Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  rspcimdv Unicode version

Theorem rspcimdv 2711
 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 2358 . 2
2 rspcimdv.1 . . 3
3 simpr 108 . . . . . . 7
43eleq1d 2151 . . . . . 6
54biimprd 156 . . . . 5
6 rspcimdv.2 . . . . 5
75, 6imim12d 73 . . . 4
82, 7spcimdv 2691 . . 3
92, 8mpid 41 . 2
101, 9syl5bi 150 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102  wal 1283   wceq 1285   wcel 1434  wral 2353 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-ral 2358  df-v 2612 This theorem is referenced by:  rspcdv  2713
 Copyright terms: Public domain W3C validator