Theorem bdcab 10798

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 10787	. 2 |- BOUNDED y e. { x | ph }
3	2	bdelir 10796	1 |- BOUNDED { x | ph }

Syntax hints:   {cab 2068  BOUNDED wbd 10761  BOUNDED wbdc 10789

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-gen 1379  ax-bd0 10762  ax-bdsb 10771

This theorem depends on definitions:  df-bi 115  df-clab 2069  df-bdc 10790

This theorem is referenced by:  bds  10800  bdcrab  10801  bdccsb  10809  bdcdif  10810  bdcun  10811  bdcin  10812  bdcpw  10818  bdcsn  10819  bdcuni  10825  bdcint  10826  bdciun  10827  bdciin  10828  bdcriota  10832  bj-bdfindis  10900