Theorem bdcab 9304

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 ph

Assertion

Ref	Expression
bdcab	|- BOUNDED {x | ph }

Proof of Theorem bdcab

Dummy variable y is distinct from all other variables.

Step	Hyp	Ref	Expression
1		bdcab.1	. . 3 |- BOUNDED ph
2	1	bdab 9293	. 2 |- BOUNDED y e. {x | ph }
3	2	bdelir 9302	1 |- BOUNDED {x | ph }

Syntax hints:   {cab 2023  BOUNDED wbd 9267  BOUNDED wbdc 9295

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-gen 1335  ax-bd0 9268  ax-bdsb 9277

This theorem depends on definitions:  df-bi 110  df-clab 2024  df-bdc 9296

This theorem is referenced by:  bds  9306  bdcrab  9307  bdccsb  9315  bdcdif  9316  bdcun  9317  bdcin  9318  bdcpw  9324  bdcsn  9325  bdcuni  9331  bdcint  9332  bdciun  9333  bdciin  9334  bdcriota  9338  bj-bdfindis  9407