Theorem bdeli 16292

Description: Inference associated with bdel 16291. Its converse is bdelir 16293. (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 16291	. 2 |- (BOUNDED A -> BOUNDED x e. A )
3	1, 2	ax-mp 5	1 |- BOUNDED x e. A

Syntax hints:   e. wcel 2200  BOUNDED wbd 16258  BOUNDED wbdc 16286

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1556

This theorem depends on definitions:  df-bi 117  df-bdc 16287

This theorem is referenced by:  bdph  16296  bdcrab  16298  bdnel  16300  bdccsb  16306  bdcdif  16307  bdcun  16308  bdcin  16309  bdss  16310  bdsnss  16319  bdciun  16324  bdciin  16325  bdinex1  16345  bj-uniex2  16362  bj-inf2vnlem3  16418