New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  sbcie2g Unicode version

Theorem sbcie2g 3079
 Description: Conversion of implicit substitution to explicit class substitution. This version of sbcie 3080 avoids a disjointness condition on by substituting twice. (Contributed by Mario Carneiro, 15-Oct-2016.)
Hypotheses
Ref Expression
sbcie2g.1
sbcie2g.2
Assertion
Ref Expression
sbcie2g
Distinct variable groups:   ,   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()   ()   (,)

Proof of Theorem sbcie2g
StepHypRef Expression
1 dfsbcq 3048 . 2
2 sbcie2g.2 . 2
3 sbsbc 3050 . . 3
4 nfv 1619 . . . 4
5 sbcie2g.1 . . . 4
64, 5sbie 2038 . . 3
73, 6bitr3i 242 . 2
81, 2, 7vtoclbg 2915 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wceq 1642  wsb 1648   wcel 1710  wsbc 3046 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-v 2861  df-sbc 3047 This theorem is referenced by:  csbie2g  3182  brab1  4684
 Copyright terms: Public domain W3C validator