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.

Step	Hyp	Ref	Expression
1		cbvcsb.1	. . . . 5
2	1	nfcri 2612	. . . 4
3		cbvcsb.2	. . . . 5
4	3	nfcri 2612	. . . 4
5		cbvcsb.3	. . . . 5
6	5	eleq2d 2527	. . . 4
7	2, 4, 6	cbvsbc 3356	. . 3
8	7	abbii 2591	. 2
9		df-csb 3435	. 2
10		df-csb 3435	. 2
11	8, 9, 10	3eqtr4i 2496	1

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