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Theorem bdccsb 9980
 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
Assertion
Ref Expression
bdccsb BOUNDED

Proof of Theorem bdccsb
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bdccsb.1 . . . . 5 BOUNDED
21bdeli 9966 . . . 4 BOUNDED
32bdsbc 9978 . . 3 BOUNDED
43bdcab 9969 . 2 BOUNDED
5 df-csb 2853 . 2
64, 5bdceqir 9964 1 BOUNDED
 Colors of variables: wff set class Syntax hints:   wcel 1393  cab 2026  wsbc 2764  csb 2852  BOUNDED wbdc 9960 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 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427  ax-ext 2022  ax-bd0 9933  ax-bdsb 9942 This theorem depends on definitions:  df-bi 110  df-clab 2027  df-cleq 2033  df-clel 2036  df-sbc 2765  df-csb 2853  df-bdc 9961 This theorem is referenced by: (None)
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