Theorem bdeli 15600

Description: Inference associated with bdel 15599. Its converse is bdelir 15601. (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 15599	. 2 |- (BOUNDED A -> BOUNDED x e. A )
3	1, 2	ax-mp 5	1 |- BOUNDED x e. A

Syntax hints:   e. wcel 2167  BOUNDED wbd 15566  BOUNDED wbdc 15594

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1524

This theorem depends on definitions:  df-bi 117  df-bdc 15595

This theorem is referenced by:  bdph  15604  bdcrab  15606  bdnel  15608  bdccsb  15614  bdcdif  15615  bdcun  15616  bdcin  15617  bdss  15618  bdsnss  15627  bdciun  15632  bdciin  15633  bdinex1  15653  bj-uniex2  15670  bj-inf2vnlem3  15726