Theorem bdeli 11394

Description: Inference associated with bdel 11393. Its converse is bdelir 11395. (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 11393	. 2 |- (BOUNDED A -> BOUNDED x e. A )
3	1, 2	ax-mp 7	1 |- BOUNDED x e. A

Syntax hints:   e. wcel 1438  BOUNDED wbd 11360  BOUNDED wbdc 11388

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-4 1445

This theorem depends on definitions:  df-bi 115  df-bdc 11389

This theorem is referenced by:  bdph  11398  bdcrab  11400  bdnel  11402  bdccsb  11408  bdcdif  11409  bdcun  11410  bdcin  11411  bdss  11412  bdsnss  11421  bdciun  11426  bdciin  11427  bdinex1  11447  bj-uniex2  11464  bj-inf2vnlem3  11524