Theorem bdeli 16377

Description: Inference associated with bdel 16376. Its converse is bdelir 16378. (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 16376	. 2 |- (BOUNDED A -> BOUNDED x e. A )
3	1, 2	ax-mp 5	1 |- BOUNDED x e. A

Syntax hints:   e. wcel 2200  BOUNDED wbd 16343  BOUNDED wbdc 16371

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1556

This theorem depends on definitions:  df-bi 117  df-bdc 16372

This theorem is referenced by:  bdph  16381  bdcrab  16383  bdnel  16385  bdccsb  16391  bdcdif  16392  bdcun  16393  bdcin  16394  bdss  16395  bdsnss  16404  bdciun  16409  bdciin  16410  bdinex1  16430  bj-uniex2  16447  bj-inf2vnlem3  16503