Theorem bdeli 13033

Description: Inference associated with bdel 13032. Its converse is bdelir 13034. (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 13032	. 2 |- (BOUNDED A -> BOUNDED x e. A )
3	1, 2	ax-mp 5	1 |- BOUNDED x e. A

Syntax hints:   e. wcel 1480  BOUNDED wbd 12999  BOUNDED wbdc 13027

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-4 1487

This theorem depends on definitions:  df-bi 116  df-bdc 13028

This theorem is referenced by:  bdph  13037  bdcrab  13039  bdnel  13041  bdccsb  13047  bdcdif  13048  bdcun  13049  bdcin  13050  bdss  13051  bdsnss  13060  bdciun  13065  bdciin  13066  bdinex1  13086  bj-uniex2  13103  bj-inf2vnlem3  13159