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Theorem bdccsb 9295
 Description: A class resulting from proper substitution of a setvar for a setvar in a bounded class is bounded. (Contributed by BJ, 16-Oct-2019.)
Hypothesis
Ref Expression
bdccsb.1 BOUNDED A
Assertion
Ref Expression
bdccsb BOUNDED y / xA

Proof of Theorem bdccsb
Dummy variable z is distinct from all other variables.
StepHypRef Expression
1 bdccsb.1 . . . . 5 BOUNDED A
21bdeli 9281 . . . 4 BOUNDED z A
32bdsbc 9293 . . 3 BOUNDED [y / x]z A
43bdcab 9284 . 2 BOUNDED {z[y / x]z A}
5 df-csb 2847 . 2 y / xA = {z[y / x]z A}
64, 5bdceqir 9279 1 BOUNDED y / xA
 Colors of variables: wff set class Syntax hints:   ∈ wcel 1390  {cab 2023  [wsbc 2758  ⦋csb 2846  BOUNDED wbdc 9275 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424  ax-ext 2019  ax-bd0 9248  ax-bdsb 9257 This theorem depends on definitions:  df-bi 110  df-clab 2024  df-cleq 2030  df-clel 2033  df-sbc 2759  df-csb 2847  df-bdc 9276 This theorem is referenced by: (None)
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