Theorem bdcab 16745

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 16734	. 2 |- BOUNDED y e. { x | ph }
3	2	bdelir 16743	1 |- BOUNDED { x | ph }

Syntax hints:   {cab 2220  BOUNDED wbd 16708  BOUNDED wbdc 16736

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 1498  ax-bd0 16709  ax-bdsb 16718

This theorem depends on definitions:  df-bi 117  df-clab 2221  df-bdc 16737

This theorem is referenced by:  bds  16747  bdcrab  16748  bdccsb  16756  bdcdif  16757  bdcun  16758  bdcin  16759  bdcpw  16765  bdcsn  16766  bdcuni  16772  bdcint  16773  bdciun  16774  bdciin  16775  bdcriota  16779  bj-bdfindis  16843