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Theorem bdcab 10356
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 10345 . 2 BOUNDED 𝑦 ∈ {𝑥𝜑}
32bdelir 10354 1 BOUNDED {𝑥𝜑}
Colors of variables: wff set class
Syntax hints:  {cab 2042  BOUNDED wbd 10319  BOUNDED wbdc 10347
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-gen 1354  ax-bd0 10320  ax-bdsb 10329
This theorem depends on definitions:  df-bi 114  df-clab 2043  df-bdc 10348
This theorem is referenced by:  bds  10358  bdcrab  10359  bdccsb  10367  bdcdif  10368  bdcun  10369  bdcin  10370  bdcpw  10376  bdcsn  10377  bdcuni  10383  bdcint  10384  bdciun  10385  bdciin  10386  bdcriota  10390  bj-bdfindis  10459
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