Theorem bdeli 15408

Description: Inference associated with bdel 15407. Its converse is bdelir 15409. (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 15407	. 2 |- (BOUNDED A -> BOUNDED x e. A )
3	1, 2	ax-mp 5	1 |- BOUNDED x e. A

Syntax hints:   e. wcel 2164  BOUNDED wbd 15374  BOUNDED wbdc 15402

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1521

This theorem depends on definitions:  df-bi 117  df-bdc 15403

This theorem is referenced by:  bdph  15412  bdcrab  15414  bdnel  15416  bdccsb  15422  bdcdif  15423  bdcun  15424  bdcin  15425  bdss  15426  bdsnss  15435  bdciun  15440  bdciin  15441  bdinex1  15461  bj-uniex2  15478  bj-inf2vnlem3  15534