Theorem bdcab 16212

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 16201	. 2 |- BOUNDED y e. { x | ph }
3	2	bdelir 16210	1 |- BOUNDED { x | ph }

Syntax hints:   {cab 2215  BOUNDED wbd 16175  BOUNDED wbdc 16203

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 1495  ax-bd0 16176  ax-bdsb 16185

This theorem depends on definitions:  df-bi 117  df-clab 2216  df-bdc 16204

This theorem is referenced by:  bds  16214  bdcrab  16215  bdccsb  16223  bdcdif  16224  bdcun  16225  bdcin  16226  bdcpw  16232  bdcsn  16233  bdcuni  16239  bdcint  16240  bdciun  16241  bdciin  16242  bdcriota  16246  bj-bdfindis  16310