Theorem csbeq2d 3834

Description: Formula-building deduction rule for class substitution. (Contributed by NM, 22-Nov-2005.) (Revised by Mario Carneiro, 1-Sep-2015.)

Hypotheses

Ref	Expression
csbeq2d.1
csbeq2d.2

Assertion

Ref	Expression
csbeq2d

Proof of Theorem csbeq2d

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		csbeq2d.1	. . . 4
2		csbeq2d.2	. . . . 5
3	2	eleq2d 2527	. . . 4
4	1, 3	sbcbid 3385	. . 3
5	4	abbidv 2593	. 2
6		df-csb 3435	. 2
7		df-csb 3435	. 2
8	5, 6, 7	3eqtr4g 2523	1

Syntax hints:  ->wi 4  =wceq 1395  F/wnf 1616  e.wcel 1818  {cab 2442  [.wsbc 3327  [_csb 3434

This theorem is referenced by:  csbeq2dv  3835

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-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-sbc 3328  df-csb 3435