Theorem bdeli 16603

Description: Inference associated with bdel 16602. Its converse is bdelir 16604. (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 16602	. 2 |- (BOUNDED A -> BOUNDED x e. A )
3	1, 2	ax-mp 5	1 |- BOUNDED x e. A

Syntax hints:   e. wcel 2203  BOUNDED wbd 16569  BOUNDED wbdc 16597

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1559

This theorem depends on definitions:  df-bi 117  df-bdc 16598

This theorem is referenced by:  bdph  16607  bdcrab  16609  bdnel  16611  bdccsb  16617  bdcdif  16618  bdcun  16619  bdcin  16620  bdss  16621  bdsnss  16630  bdciun  16635  bdciin  16636  bdinex1  16656  bj-uniex2  16673  bj-inf2vnlem3  16729