Theorem bdcab 16789

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 16778	. 2 |- BOUNDED y e. { x | ph }
3	2	bdelir 16787	1 |- BOUNDED { x | ph }

Syntax hints:   {cab 2224  BOUNDED wbd 16752  BOUNDED wbdc 16780

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 1502  ax-bd0 16753  ax-bdsb 16762

This theorem depends on definitions:  df-bi 117  df-clab 2225  df-bdc 16781

This theorem is referenced by:  bds  16791  bdcrab  16792  bdccsb  16800  bdcdif  16801  bdcun  16802  bdcin  16803  bdcpw  16809  bdcsn  16810  bdcuni  16816  bdcint  16817  bdciun  16818  bdciin  16819  bdcriota  16823  bj-bdfindis  16887