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Theorem bdceqi 10777
Description: A class equal to a bounded one is bounded. Note the use of ax-ext 2064. See also bdceqir 10778. (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 10776 . 2  |-  (BOUNDED  A  <-> BOUNDED  B )
41, 3mpbi 143 1  |- BOUNDED  B
Colors of variables: wff set class
Syntax hints:    = wceq 1285  BOUNDED wbdc 10774
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-17 1460  ax-ial 1468  ax-ext 2064  ax-bd0 10747
This theorem depends on definitions:  df-bi 115  df-cleq 2075  df-clel 2078  df-bdc 10775
This theorem is referenced by:  bdceqir  10778  bds  10785  bdcuni  10810
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