MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  csbeq2d Unicode version

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.
StepHypRef Expression
1 csbeq2d.1 . . . 4
2 csbeq2d.2 . . . . 5
32eleq2d 2527 . . . 4
41, 3sbcbid 3385 . . 3
54abbidv 2593 . 2
6 df-csb 3435 . 2
7 df-csb 3435 . 2
85, 6, 73eqtr4g 2523 1
Colors of variables: wff setvar class
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
  Copyright terms: Public domain W3C validator