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Theorem csbeq2d 3275
 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 2503 . . . 4
41, 3sbcbid 3214 . . 3
54abbidv 2550 . 2
6 df-csb 3252 . 2
7 df-csb 3252 . 2
85, 6, 73eqtr4g 2493 1
 Colors of variables: wff set class Syntax hints:   wi 4  wnf 1553   wceq 1652   wcel 1725  cab 2422  wsbc 3161  csb 3251 This theorem is referenced by:  csbeq2dv  3276 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-sbc 3162  df-csb 3252
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