Theorem bdeli 14683

Description: Inference associated with bdel 14682. Its converse is bdelir 14684. (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 14682	. 2 |- (BOUNDED A -> BOUNDED x e. A )
3	1, 2	ax-mp 5	1 |- BOUNDED x e. A

Syntax hints:   e. wcel 2148  BOUNDED wbd 14649  BOUNDED wbdc 14677

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1510

This theorem depends on definitions:  df-bi 117  df-bdc 14678

This theorem is referenced by:  bdph  14687  bdcrab  14689  bdnel  14691  bdccsb  14697  bdcdif  14698  bdcun  14699  bdcin  14700  bdss  14701  bdsnss  14710  bdciun  14715  bdciin  14716  bdinex1  14736  bj-uniex2  14753  bj-inf2vnlem3  14809