Theorem bdeli 16444

Description: Inference associated with bdel 16443. Its converse is bdelir 16445. (Contributed by BJ, 3-Oct-2019.)

Hypothesis

Ref	Expression
bdeli.1	|- BOUNDED A

Assertion

Ref	Expression
bdeli	|- BOUNDED x e. A

Distinct variable group:   x, A

Proof of Theorem bdeli

Step	Hyp	Ref	Expression
1		bdeli.1	. 2 |- BOUNDED A
2		bdel 16443	. 2 |- (BOUNDED A -> BOUNDED x e. A )
3	1, 2	ax-mp 5	1 |- BOUNDED x e. A

Syntax hints:   e. wcel 2202  BOUNDED wbd 16410  BOUNDED wbdc 16438

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1558

This theorem depends on definitions:  df-bi 117  df-bdc 16439

This theorem is referenced by:  bdph  16448  bdcrab  16450  bdnel  16452  bdccsb  16458  bdcdif  16459  bdcun  16460  bdcin  16461  bdss  16462  bdsnss  16471  bdciun  16476  bdciin  16477  bdinex1  16497  bj-uniex2  16514  bj-inf2vnlem3  16570