Theorem bdeli 16755

Description: Inference associated with bdel 16754. Its converse is bdelir 16756. (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 16754	. 2 |- (BOUNDED A -> BOUNDED x e. A )
3	1, 2	ax-mp 5	1 |- BOUNDED x e. A

Syntax hints:   e. wcel 2205  BOUNDED wbd 16721  BOUNDED wbdc 16749

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1559

This theorem depends on definitions:  df-bi 117  df-bdc 16750

This theorem is referenced by:  bdph  16759  bdcrab  16761  bdnel  16763  bdccsb  16769  bdcdif  16770  bdcun  16771  bdcin  16772  bdss  16773  bdsnss  16782  bdciun  16787  bdciin  16788  bdinex1  16808  bj-uniex2  16825  bj-inf2vnlem3  16881