New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  sbc2iedv Unicode version

Theorem sbc2iedv 3114
 Description: Conversion of implicit substitution to explicit class substitution. (Contributed by NM, 16-Dec-2008.) (Proof shortened by Mario Carneiro, 18-Oct-2016.)
Hypotheses
Ref Expression
sbc2iedv.1
sbc2iedv.2
sbc2iedv.3
Assertion
Ref Expression
sbc2iedv
Distinct variable groups:   ,,   ,   ,,   ,,
Allowed substitution hints:   (,)   ()

Proof of Theorem sbc2iedv
StepHypRef Expression
1 sbc2iedv.1 . . 3
21a1i 10 . 2
3 sbc2iedv.2 . . . 4
43a1i 10 . . 3
5 sbc2iedv.3 . . . 4
65impl 603 . . 3
74, 6sbcied 3082 . 2
82, 7sbcied 3082 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358   wceq 1642   wcel 1710  cvv 2859  wsbc 3046 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-3an 936  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-v 2861  df-sbc 3047 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator