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Theorem bdab 10814
Description: Membership in a class defined by class abstraction using a bounded formula, is a bounded formula. (Contributed by BJ, 3-Oct-2019.)
Hypothesis
Ref Expression
bdab.1 BOUNDED 𝜑
Assertion
Ref Expression
bdab BOUNDED 𝑥 ∈ {𝑦𝜑}

Proof of Theorem bdab
StepHypRef Expression
1 bdab.1 . . 3 BOUNDED 𝜑
21ax-bdsb 10798 . 2 BOUNDED [𝑥 / 𝑦]𝜑
3 df-clab 2069 . 2 (𝑥 ∈ {𝑦𝜑} ↔ [𝑥 / 𝑦]𝜑)
42, 3bd0r 10801 1 BOUNDED 𝑥 ∈ {𝑦𝜑}
Colors of variables: wff set class
Syntax hints:  wcel 1434  [wsb 1686  {cab 2068  BOUNDED wbd 10788
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-bd0 10789  ax-bdsb 10798
This theorem depends on definitions:  df-bi 115  df-clab 2069
This theorem is referenced by:  bdcab  10825  bdsbcALT  10835
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