Theorem bdeli 15056

Description: Inference associated with bdel 15055. Its converse is bdelir 15057. (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 15055	. 2 |- (BOUNDED A -> BOUNDED x e. A )
3	1, 2	ax-mp 5	1 |- BOUNDED x e. A

Syntax hints:   e. wcel 2160  BOUNDED wbd 15022  BOUNDED wbdc 15050

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 15051

This theorem is referenced by:  bdph  15060  bdcrab  15062  bdnel  15064  bdccsb  15070  bdcdif  15071  bdcun  15072  bdcin  15073  bdss  15074  bdsnss  15083  bdciun  15088  bdciin  15089  bdinex1  15109  bj-uniex2  15126  bj-inf2vnlem3  15182