Theorem bdeli 13846

Description: Inference associated with bdel 13845. Its converse is bdelir 13847. (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 13845	. 2 |- (BOUNDED A -> BOUNDED x e. A )
3	1, 2	ax-mp 5	1 |- BOUNDED x e. A

Syntax hints:   e. wcel 2141  BOUNDED wbd 13812  BOUNDED wbdc 13840

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-4 1503

This theorem depends on definitions:  df-bi 116  df-bdc 13841

This theorem is referenced by:  bdph  13850  bdcrab  13852  bdnel  13854  bdccsb  13860  bdcdif  13861  bdcun  13862  bdcin  13863  bdss  13864  bdsnss  13873  bdciun  13878  bdciin  13879  bdinex1  13899  bj-uniex2  13916  bj-inf2vnlem3  13972