Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  csbie2g Structured version   Unicode version

Theorem csbie2g 3289
 Description: Conversion of implicit substitution to explicit class substitution. This version of sbcie 3187 avoids a disjointness condition on by substituting twice. (Contributed by Mario Carneiro, 11-Nov-2016.)
Hypotheses
Ref Expression
csbie2g.1
csbie2g.2
Assertion
Ref Expression
csbie2g
Distinct variable groups:   ,   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()   ()   (,)

Proof of Theorem csbie2g
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-csb 3244 . 2
2 csbie2g.1 . . . . 5
32eleq2d 2502 . . . 4
4 csbie2g.2 . . . . 5
54eleq2d 2502 . . . 4
63, 5sbcie2g 3186 . . 3
76abbi1dv 2551 . 2
81, 7syl5eq 2479 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725  cab 2421  wsbc 3153  csb 3243 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-sbc 3154  df-csb 3244
 Copyright terms: Public domain W3C validator