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Theorem bdcab 14604
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 14593 . 2 BOUNDED 𝑦 ∈ {𝑥𝜑}
32bdelir 14602 1 BOUNDED {𝑥𝜑}
Colors of variables: wff set class
Syntax hints:  {cab 2163  BOUNDED wbd 14567  BOUNDED wbdc 14595
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-gen 1449  ax-bd0 14568  ax-bdsb 14577
This theorem depends on definitions:  df-bi 117  df-clab 2164  df-bdc 14596
This theorem is referenced by:  bds  14606  bdcrab  14607  bdccsb  14615  bdcdif  14616  bdcun  14617  bdcin  14618  bdcpw  14624  bdcsn  14625  bdcuni  14631  bdcint  14632  bdciun  14633  bdciin  14634  bdcriota  14638  bj-bdfindis  14702
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