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

Theorem csbie2g 3403
 Description: Conversion of implicit substitution to explicit class substitution. This version of csbie 3398 avoids a disjointness condition on and 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 3373 . 2
2 csbie2g.1 . . . . 5
32eleq2d 2472 . . . 4
4 csbie2g.2 . . . . 5
54eleq2d 2472 . . . 4
63, 5sbcie2g 3310 . . 3
76abbi1dv 2540 . 2
81, 7syl5eq 2455 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1405   wcel 1842  cab 2387  wsbc 3276  csb 3372 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380 This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-v 3060  df-sbc 3277  df-csb 3373 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator