Theorem bdeli 9966

Description: Inference associated with bdel 9965. Its converse is bdelir 9967. (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 9965	. 2 |- (BOUNDED A -> BOUNDED x e. A )
3	1, 2	ax-mp 7	1 |- BOUNDED x e. A

Syntax hints:   e. wcel 1393  BOUNDED wbd 9932  BOUNDED wbdc 9960

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-4 1400

This theorem depends on definitions:  df-bi 110  df-bdc 9961

This theorem is referenced by:  bdph  9970  bdcrab  9972  bdnel  9974  bdccsb  9980  bdcdif  9981  bdcun  9982  bdcin  9983  bdss  9984  bdsnss  9993  bdciun  9998  bdciin  9999  bdinex1  10019  bj-uniex2  10036  bj-inf2vnlem3  10097