Theorem bdcab 14686

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 14675	. 2 |- BOUNDED y e. { x | ph }
3	2	bdelir 14684	1 |- BOUNDED { x | ph }

Syntax hints:   {cab 2163  BOUNDED wbd 14649  BOUNDED wbdc 14677

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 1449  ax-bd0 14650  ax-bdsb 14659

This theorem depends on definitions:  df-bi 117  df-clab 2164  df-bdc 14678

This theorem is referenced by:  bds  14688  bdcrab  14689  bdccsb  14697  bdcdif  14698  bdcun  14699  bdcin  14700  bdcpw  14706  bdcsn  14707  bdcuni  14713  bdcint  14714  bdciun  14715  bdciin  14716  bdcriota  14720  bj-bdfindis  14784