Theorem bdcab 13218

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 13207	. 2 |- BOUNDED y e. { x | ph }
3	2	bdelir 13216	1 |- BOUNDED { x | ph }

Syntax hints:   {cab 2126  BOUNDED wbd 13181  BOUNDED wbdc 13209

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 1426  ax-bd0 13182  ax-bdsb 13191

This theorem depends on definitions:  df-bi 116  df-clab 2127  df-bdc 13210

This theorem is referenced by:  bds  13220  bdcrab  13221  bdccsb  13229  bdcdif  13230  bdcun  13231  bdcin  13232  bdcpw  13238  bdcsn  13239  bdcuni  13245  bdcint  13246  bdciun  13247  bdciin  13248  bdcriota  13252  bj-bdfindis  13316