Theorem bdcab 16295

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 16284	. 2 |- BOUNDED y e. { x | ph }
3	2	bdelir 16293	1 |- BOUNDED { x | ph }

Syntax hints:   {cab 2215  BOUNDED wbd 16258  BOUNDED wbdc 16286

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 16259  ax-bdsb 16268

This theorem depends on definitions:  df-bi 117  df-clab 2216  df-bdc 16287

This theorem is referenced by:  bds  16297  bdcrab  16298  bdccsb  16306  bdcdif  16307  bdcun  16308  bdcin  16309  bdcpw  16315  bdcsn  16316  bdcuni  16322  bdcint  16323  bdciun  16324  bdciin  16325  bdcriota  16329  bj-bdfindis  16393