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Theorem bdcab 13849
Description: A class defined by class abstraction using a bounded formula is bounded. (Contributed by BJ, 6-Oct-2019.)
Hypothesis
Ref Expression
bdcab.1 BOUNDED 𝜑
Assertion
Ref Expression
bdcab BOUNDED {𝑥𝜑}

Proof of Theorem bdcab
Dummy variable 𝑦 is distinct from all other variables.
StepHypRef Expression
1 bdcab.1 . . 3 BOUNDED 𝜑
21bdab 13838 . 2 BOUNDED 𝑦 ∈ {𝑥𝜑}
32bdelir 13847 1 BOUNDED {𝑥𝜑}
Colors of variables: wff set class
Syntax hints:  {cab 2156  BOUNDED wbd 13812  BOUNDED wbdc 13840
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-gen 1442  ax-bd0 13813  ax-bdsb 13822
This theorem depends on definitions:  df-bi 116  df-clab 2157  df-bdc 13841
This theorem is referenced by:  bds  13851  bdcrab  13852  bdccsb  13860  bdcdif  13861  bdcun  13862  bdcin  13863  bdcpw  13869  bdcsn  13870  bdcuni  13876  bdcint  13877  bdciun  13878  bdciin  13879  bdcriota  13883  bj-bdfindis  13947
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