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Theorem csbeq2 3030
 Description: Substituting into equivalent classes gives equivalent results. (Contributed by Giovanni Mascellani, 9-Apr-2018.)
Assertion
Ref Expression
csbeq2

Proof of Theorem csbeq2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eleq2 2204 . . . . 5
21alimi 1432 . . . 4
3 sbcbi2 2962 . . . 4
42, 3syl 14 . . 3
54abbidv 2258 . 2
6 df-csb 3007 . 2
7 df-csb 3007 . 2
85, 6, 73eqtr4g 2198 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104  wal 1330   wceq 1332   wcel 1481  cab 2126  wsbc 2912  csb 3006 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 1483  ax-11 1485  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-sbc 2913  df-csb 3007 This theorem is referenced by:  prodeq2w  11356
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