Theorem bdeli 10888

Description: Inference associated with bdel 10887. Its converse is bdelir 10889. (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 10887	. 2 |- (BOUNDED A -> BOUNDED x e. A )
3	1, 2	ax-mp 7	1 |- BOUNDED x e. A

Syntax hints:   e. wcel 1434  BOUNDED wbd 10854  BOUNDED wbdc 10882

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-4 1441

This theorem depends on definitions:  df-bi 115  df-bdc 10883

This theorem is referenced by:  bdph  10892  bdcrab  10894  bdnel  10896  bdccsb  10902  bdcdif  10903  bdcun  10904  bdcin  10905  bdss  10906  bdsnss  10915  bdciun  10920  bdciin  10921  bdinex1  10941  bj-uniex2  10958  bj-inf2vnlem3  11018