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Theorem bdceqi 14455
Description: A class equal to a bounded one is bounded. Note the use of ax-ext 2159. See also bdceqir 14456. (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 14454 . 2  |-  (BOUNDED  A  <-> BOUNDED  B )
41, 3mpbi 145 1  |- BOUNDED  B
Colors of variables: wff set class
Syntax hints:    = wceq 1353  BOUNDED wbdc 14452
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-17 1526  ax-ial 1534  ax-ext 2159  ax-bd0 14425
This theorem depends on definitions:  df-bi 117  df-cleq 2170  df-clel 2173  df-bdc 14453
This theorem is referenced by:  bdceqir  14456  bds  14463  bdcuni  14488
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