Theorem bdeli 13215

Description: Inference associated with bdel 13214. Its converse is bdelir 13216. (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 13214	. 2 |- (BOUNDED A -> BOUNDED x e. A )
3	1, 2	ax-mp 5	1 |- BOUNDED x e. A

Syntax hints:   e. wcel 1481  BOUNDED wbd 13181  BOUNDED wbdc 13209

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-4 1488

This theorem depends on definitions:  df-bi 116  df-bdc 13210

This theorem is referenced by:  bdph  13219  bdcrab  13221  bdnel  13223  bdccsb  13229  bdcdif  13230  bdcun  13231  bdcin  13232  bdss  13233  bdsnss  13242  bdciun  13247  bdciin  13248  bdinex1  13268  bj-uniex2  13285  bj-inf2vnlem3  13341