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

Theorem spcimdv 3191
 Description: Restricted specialization, using implicit substitution. (Contributed by Mario Carneiro, 4-Jan-2017.)
Hypotheses
Ref Expression
spcimdv.1
spcimdv.2
Assertion
Ref Expression
spcimdv
Distinct variable groups:   ,   ,   ,

Proof of Theorem spcimdv
StepHypRef Expression
1 spcimdv.2 . . . 4
21ex 434 . . 3
32alrimiv 1719 . 2
4 spcimdv.1 . 2
5 nfv 1707 . . 3
6 nfcv 2619 . . 3
75, 6spcimgft 3185 . 2
83, 4, 7sylc 60 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  A.wal 1393  =wceq 1395  e.wcel 1818 This theorem is referenced by:  spcdv  3192  spcimedv  3193  rspcimdv  3211  mrieqv2d  15036  mreexexlemd  15041 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-v 3111
 Copyright terms: Public domain W3C validator