Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >   Mathboxes  >  bdceqi GIF version

Theorem bdceqi 9963
Description: A class equal to a bounded one is bounded. Note the use of ax-ext 2022. See also bdceqir 9964. (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 9962 . 2 (BOUNDED 𝐴BOUNDED 𝐵)
41, 3mpbi 133 1 BOUNDED 𝐵
Colors of variables: wff set class
Syntax hints:   = wceq 1243  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
This theorem depends on definitions:  df-bi 110  df-cleq 2033  df-clel 2036  df-bdc 9961
This theorem is referenced by:  bdceqir  9964  bds  9971  bdcuni  9996
  Copyright terms: Public domain W3C validator