Theorem bdcab 16973

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 16962	. 2 |- BOUNDED y e. { x | ph }
3	2	bdelir 16971	1 |- BOUNDED { x | ph }

This proof depends on syntax axioms:   {cab 2224  BOUNDED wbd 16936  BOUNDED wbdc 16964

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-gen 1502  ax-bd0 16937  ax-bdsb 16946

This proof depends on definitions:  df-bi 117  df-clab 2225  df-bdc 16965

This theorem is used by:  bds  16975  bdcrab  16976  bdccsb  16984  bdcdif  16985  bdcun  16986  bdcin  16987  bdcpw  16993  bdcsn  16994  bdcuni  17000  bdcint  17001  bdciun  17002  bdciin  17003  bdcriota  17007  bj-bdfindis  17071