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Theorem bdceqi 12968
Description: A class equal to a bounded one is bounded. Note the use of ax-ext 2099. See also bdceqir 12969. (Contributed by BJ, 3-Oct-2019.)
Hypotheses
Ref Expression
bdceqi.min  |- BOUNDED  A
bdceqi.maj  |-  A  =  B
Assertion
Ref Expression
bdceqi  |- BOUNDED  B

Proof of Theorem bdceqi
StepHypRef Expression
1 bdceqi.min . 2  |- BOUNDED  A
2 bdceqi.maj . . 3  |-  A  =  B
32bdceq 12967 . 2  |-  (BOUNDED  A  <-> BOUNDED  B )
41, 3mpbi 144 1  |- BOUNDED  B
Colors of variables: wff set class
Syntax hints:    = wceq 1316  BOUNDED wbdc 12965
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 1408  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-4 1472  ax-17 1491  ax-ial 1499  ax-ext 2099  ax-bd0 12938
This theorem depends on definitions:  df-bi 116  df-cleq 2110  df-clel 2113  df-bdc 12966
This theorem is referenced by:  bdceqir  12969  bds  12976  bdcuni  13001
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