Theorem bdeli 16501

Description: Inference associated with bdel 16500. Its converse is bdelir 16502. (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 16500	. 2 |- (BOUNDED A -> BOUNDED x e. A )
3	1, 2	ax-mp 5	1 |- BOUNDED x e. A

Syntax hints:   e. wcel 2201  BOUNDED wbd 16467  BOUNDED wbdc 16495

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1558

This theorem depends on definitions:  df-bi 117  df-bdc 16496

This theorem is referenced by:  bdph  16505  bdcrab  16507  bdnel  16509  bdccsb  16515  bdcdif  16516  bdcun  16517  bdcin  16518  bdss  16519  bdsnss  16528  bdciun  16533  bdciin  16534  bdinex1  16554  bj-uniex2  16571  bj-inf2vnlem3  16627