Theorem bdeli 16665

Description: Inference associated with bdel 16664. Its converse is bdelir 16666. (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 16664	. 2 |- (BOUNDED A -> BOUNDED x e. A )
3	1, 2	ax-mp 5	1 |- BOUNDED x e. A

Syntax hints:   e. wcel 2205  BOUNDED wbd 16631  BOUNDED wbdc 16659

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 16660

This theorem is referenced by:  bdph  16669  bdcrab  16671  bdnel  16673  bdccsb  16679  bdcdif  16680  bdcun  16681  bdcin  16682  bdss  16683  bdsnss  16692  bdciun  16697  bdciin  16698  bdinex1  16718  bj-uniex2  16735  bj-inf2vnlem3  16791