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Theorem csbeq2d 3034
 Description: Formula-building deduction 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 2211 . . . 4
41, 3sbcbid 2972 . . 3
54abbidv 2259 . 2
6 df-csb 3010 . 2
7 df-csb 3010 . 2
85, 6, 73eqtr4g 2199 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1332  wnf 1437   wcel 2112  cab 2127  wsbc 2915  csb 3009 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-11 1483  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2123 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1732  df-clab 2128  df-cleq 2134  df-clel 2137  df-sbc 2916  df-csb 3010 This theorem is referenced by:  csbeq2dv  3035
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