MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  rspcimdv Unicode version

Theorem rspcimdv 3211
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:   ,   ,   ,   ,

Proof of Theorem rspcimdv
StepHypRef Expression
1 df-ral 2812 . 2
2 rspcimdv.1 . . 3
3 simpr 461 . . . . . . 7
43eleq1d 2526 . . . . . 6
54biimprd 223 . . . . 5
6 rspcimdv.2 . . . . 5
75, 6imim12d 74 . . . 4
82, 7spcimdv 3191 . . 3
92, 8mpid 41 . 2
101, 9syl5bi 217 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  A.wal 1393  =wceq 1395  e.wcel 1818  A.wral 2807
This theorem is referenced by:  rspcimedv  3212  rspcdv  3213  wrd2ind  12703  mreexd  15039  mreexexlemd  15041  catcocl  15082  catass  15083  moni  15131  subccocl  15214  funcco  15240  fullfo  15281  fthf1  15286  nati  15324  acsfiindd  15807  chpscmat  19343  sizeusglecusglem1  24484  friendshipgt3  25121  lmxrge0  27934  funressnfv  32213
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-v 3111
  Copyright terms: Public domain W3C validator