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

Theorem cbvcsb 3439
 Description: Change bound variables in a class substitution. Interestingly, this does not require any bound variable conditions on . (Contributed by Jeff Hankins, 13-Sep-2009.) (Revised by Mario Carneiro, 11-Dec-2016.)
Hypotheses
Ref Expression
cbvcsb.1
cbvcsb.2
cbvcsb.3
Assertion
Ref Expression
cbvcsb

Proof of Theorem cbvcsb
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 cbvcsb.1 . . . . 5
21nfcri 2612 . . . 4
3 cbvcsb.2 . . . . 5
43nfcri 2612 . . . 4
5 cbvcsb.3 . . . . 5
65eleq2d 2527 . . . 4
72, 4, 6cbvsbc 3356 . . 3
87abbii 2591 . 2
9 df-csb 3435 . 2
10 df-csb 3435 . 2
118, 9, 103eqtr4i 2496 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  =wceq 1395  e.wcel 1818  {cab 2442  F/_wnfc 2605  [.wsbc 3327  [_csb 3434 This theorem is referenced by:  cbvcsbv  3440  cbvsum  13517  cbvprod  13722  measiuns  28188 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-or 370  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-sbc 3328  df-csb 3435
 Copyright terms: Public domain W3C validator